Binary-coded decimal - Knowledge (XXG)

3965:

of 1111 (F). ILE RPG uses 1111 (F) for positive and 1101 (D) for negative. These match the EBCDIC zone for digits without a sign overpunch. In packed BCD, the number 127 is represented by 0001 0010 0111 1100 (127C) and −127 is represented by 0001 0010 0111 1101 (127D). Burroughs systems used 1101 (D) for negative, and any other value is considered a positive sign value (the processors will normalize a positive sign to 1100 (C)).

5607: 5665: 5566: 40: 8688:(bits 0 through 3). The high half-byte (bits 4 through 7) can be any value during addition and subtraction, but must be zero during multiplication and division. Packed BCD integers allow two BCD digits to be contained in one byte. Here, the digit in the high half-byte is more significant than the digit in the low half-byte. When operating on BCD integers in 3945:, i.e. with the more significant digit in the upper half of each byte, and with the leftmost byte (residing at the lowest memory address) containing the most significant digits of the packed decimal value. The lower nibble of the rightmost byte is usually used as the sign flag, although some unsigned representations lack a sign flag. 160:, is its more accurate representation and rounding of decimal quantities, as well as its ease of conversion into conventional human-readable representations. Its principal drawbacks are a slight increase in the complexity of the circuits needed to implement basic arithmetic as well as slightly less dense storage. 6216:

This representation allows rapid multiplication and division, but may require shifting by a power of 10 during addition and subtraction to align the decimal points. It is appropriate for applications with a fixed number of decimal places that do not then require this adjustment—particularly financial

4997:

If there are a different number of nibbles being added together (such as 1053 − 2), the number with the fewer digits must first be prefixed with zeros before taking the ten's complement or subtracting. So, with 1053 − 2, 2 would have to first be represented as 0002 in BCD, and the ten's complement of

3964:

Other allowed signs are 1010 (A) and 1110 (E) for positive and 1011 (B) for negative. IBM System/360 processors will use the 1010 (A) and 1011 (B) signs if the A bit is set in the PSW, for the ASCII-8 standard that never passed. Most implementations also provide unsigned BCD values with a sign nibble

8715:

form; they are distinguished from positive decimal integers only by the sign bit. The range of decimal integers that can be encoded in this format is −10 + 1 to 10 − 1. The decimal integer format exists in memory only. When a decimal integer is loaded in an x87 FPU data register, it is automatically

5845:

Many non-integral values, such as decimal 0.2, have an infinite place-value representation in binary (.001100110011...) but have a finite place-value in binary-coded decimal (0.0010). Consequently, a system based on binary-coded decimal representations of decimal fractions avoids errors representing

5779:

BCD is common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor. By employing BCD, the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate

4993:

Thus the result of the subtraction is 1001 1001 0010 0101 (−925). To confirm the result, note that the first digit is 9, which means negative. This seems to be correct since 357 − 432 should result in a negative number. The remaining nibbles are BCD, so 1001 0010 0101 is 925. The ten's complement of

4922:

10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number. In BCD as in decimal, there cannot exist a value greater than 9 (1001) per digit. To correct this, 6 (0110) is added to the total, and then the result

7423:

for n = 4, or, in fact, with any set of ten code combinations which include all eight with an even (or all eight with an odd) number of "1's." The second and third rows of Table II list the average and peak decimal change per undetected single binary error, and have been derived using the equations

6208:

If errors in representation and computation are more important than the speed of conversion to and from display, a scaled binary representation may be used, which stores a decimal number as a binary-encoded integer and a binary-encoded signed decimal exponent. For example, 0.2 can be represented as

5787:

to build a metering circuit, for example. If the numeric quantity were stored and manipulated as pure binary, interfacing with such a display would require complex circuitry. Therefore, in cases where the calculations are relatively simple, working throughout with BCD can lead to an overall simpler

5292:

that can perform arithmetic directly on packed BCD data and convert between packed BCD data and other integer representations. The VAX's packed BCD format is compatible with that on IBM System/360 and IBM's later compatible processors. The MicroVAX and later VAX implementations dropped this ability

4986:

Since BCD is a form of decimal representation, several of the digit sums above are invalid. In the event that an invalid entry (any BCD digit greater than 1001) exists, 6 is added to generate a carry bit and cause the sum to become a valid entry. So, adding 6 to the invalid entries results in the

5791:

The same argument applies when hardware of this type uses an embedded microcontroller or other small processor. Often, representing numbers internally in BCD format results in smaller code, since a conversion from or to binary representation can be expensive on such limited processors. For these

4270:

For signed zoned decimal values, the rightmost (least significant) zone nibble holds the sign digit, which is the same set of values that are used for signed packed decimal numbers (see above). Thus a zoned decimal value encoded as the hex bytes F1 F2 D3 represents the signed decimal value −123:

4266:

numeric representations. Each decimal digit is stored in one byte, with the lower four bits encoding the digit in BCD form. The upper four bits, called the "zone" bits, are usually set to a fixed value so that the byte holds a character value corresponding to the digit. EBCDIC systems use a zone

5275:

processors. In these products, the BCD is usually zoned BCD (as in EBCDIC or ASCII), packed BCD (two decimal digits per byte), or "pure" BCD encoding (one decimal digit stored as BCD in the low four bits of each byte). All of these are used within hardware registers and processing units, and in

4915:

by first adding in binary, and then converting to BCD afterwards. Conversion of the simple sum of two digits can be done by adding 6 (that is, 16 − 10) when the five-bit result of adding a pair of digits has a value greater than 9. The reason for adding 6 is that there are 16 possible 4-bit BCD

8296:, for Special Summer Programs held in 1956 and 1957. The code Susskind actually presented in his work as "reading-type code" is shown as code type II here, whereas the type I code is a minor derivation with the two most significant bit columns swapped to better illustrate symmetries.) 8108: 4200:

representations for negative numbers offer an alternative approach to encoding the sign of packed (and other) BCD numbers. In this case, positive numbers always have a most significant digit between 0 and 4 (inclusive), while negative numbers are represented by the 10's complement of the

5875:

10 bits is 1.204). When packed so that three digits are encoded in ten bits, the storage overhead is greatly reduced, at the expense of an encoding that is unaligned with the 8-bit byte boundaries common on existing hardware, resulting in slower implementations on these

4158:

is made trivial, as no arithmetic operations are required. The extra storage requirements are usually offset by the need for the accuracy and compatibility with calculator or hand calculation that fixed-point decimal arithmetic provides. Denser packings of

5863:

require extra logic to cause them to wrap and generate a carry early. Also, 15 to 20 per cent more circuitry is needed for BCD add compared to pure binary. Multiplication requires the use of algorithms that are somewhat more complex than shift-mask-add (a

7471: 7469: 7467: 7465: 7463: 7461: 7459: 7457: 7455: 7453: 7451: 7999:

The cyclic code is advantageous mainly in the use of relay circuits, for then a sticky relay will not give a false state as it is delayed in going from one cyclic number to the next. There are many other cyclic codes that have this property.

5327:

There are tricks for implementing packed BCD and zoned decimal add–or–subtract operations using short but difficult to understand sequences of word-parallel logic and binary arithmetic operations. For example, the following code (written in

4228:

The decimal point is not actually stored in memory, as the packed BCD storage format does not provide for it. Its location is simply known to the compiler, and the generated code acts accordingly for the various arithmetic operations.

7401:. Convention Record of the I.R.E., 1954 National Convention, Part 4 - Electronic Computers and Information Theory. Session 19: Information Theory III - Speed and Computation. Stanford Research Institute, Stanford, California, USA: 4267:

value of 1111 (hex F); this yields bytes in the range F0 to F9 (hex), which are the EBCDIC codes for the characters "0" through "9". Similarly, ASCII systems use a zone value of 0011 (hex 3), giving character codes 30 to 39 (hex).

3907:(but formatting routines might replace or remove leading zeros). Packed BCD is more efficient in storage usage than unpacked BCD; encoding the same number (with the leading zero) in unpacked format would consume twice the storage. 4237:

If a decimal digit requires four bits, then three decimal digits require 12 bits. However, since 2 (1,024) is greater than 10 (1,000), if three decimal digits are encoded together, only 10 bits are needed. Two such encodings are

6659: 3948:

As an example, a 4-byte value consists of 8 nibbles, wherein the upper 7 nibbles store the digits of a 7-digit decimal value, and the lowest nibble indicates the sign of the decimal integer value. Standard sign values are 1100

4932:

This technique can be extended to adding multiple digits by adding in groups from right to left, propagating the second digit as a carry, always comparing the 5-bit result of each digit-pair sum to 9. Some CPUs provide a

4204:

As a result, this system allows for 32-bit packed BCD numbers to range from −50,000,000 to +49,999,999, and −1 is represented as 99999999. (As with two's complement binary numbers, the range is not symmetric about zero.)

7418:

The last column , labeled "Best," gives the maximum fraction possible with any code—namely 0.60—half again better than any conventional code. This extremal is reached with the ten heavily-marked vertices of the graph of

110:

BCD typically encodes two digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9. The precise four-bit encoding, however, may vary for technical reasons (e.g.

5229:

BCD) of the 10-digit word, with the "zone" in the left digit and the "digit" in the right digit. Input/output translation hardware converted between the internal digit pairs and the external standard 6-bit BCD codes.

5323:

In more recent computers such capabilities are almost always implemented in software rather than the CPU's instruction set, but BCD numeric data are still extremely common in commercial and financial applications.

4131:

Like character strings, the first byte of the packed decimal – that with the most significant two digits – is usually stored in the lowest address in memory, independent of the

8981:"Digital cellular telecommunications system (Phase 2+) (GSM); Universal Mobile Telecommunications System (UMTS); LTE; 5G; Numbering, addressing and identification (3GPP TS 23.003 version 16.8.0 Release 16)" 8627: 4976:

of 432, and then adding one. So, 999 − 432 = 567, and 567 + 1 = 568. By preceding 568 in BCD by the negative sign code, the number −432 can be represented. So, −432 in signed BCD is 1001 0101 0110 1000.

7436:= |i − j| i,j = 0, 1, … 9. Again, the "Best" arrangement possible (the same for average and peak), one of which is shown in Fig. 4, is substantially better than the conventional codes. Fig. 4 6596: 8275: 5856:

Practical existing implementations of BCD are typically slower than operations on binary representations, especially on embedded systems, due to limited processor support for native BCD operations.

7984: 8270:

Susskind, Alfred Kriss; Ward, John Erwin (1958-03-28) . "III.F. Unit-Distance Codes / VI.E.2. Reflected Binary Codes". Written at Cambridge, Massachusetts, USA. In Susskind, Alfred Kriss (ed.).

4219:

For example, a packed decimal value encoded with the bytes 12 34 56 7C represents the fixed-point value +1,234.567 when the implied decimal point is located between the fourth and fifth digits:

5293:

from the CPU but retained code compatibility with earlier machines by implementing the missing instructions in an operating system-supplied software library. This is invoked automatically via

4216:

decimal numbers are supported by some programming languages (such as COBOL and PL/I). These languages allow the programmer to specify an implicit decimal point in front of one of the digits.

4125:

For example, a 4-byte (32-bit) word can hold seven decimal digits plus a sign and can represent values ranging from ±9,999,999. Thus the number −1,234,567 is 7 digits wide and is encoded as:

5160:. This allows the circuitry to convert between the punched card format and the internal storage format to be very simple with only a few special cases. One important special case is digit 4170:

programming language as the "COMPUTATIONAL-3" (an IBM extension adopted by many other compiler vendors) or "PACKED-DECIMAL" (part of the 1985 COBOL standard) data type. It is supported in

6458:

Code states (shown in black) outside the decimal range 0–9 indicate additional states of the non-BCD variant of the code. In the BCD code variant discussed here, they are pseudo-tetrades.

4895:

For example, given a six-byte signed zoned decimal value with an implied decimal point to the right of the fourth digit, the hex bytes F1 F2 F7 F9 F5 C0 represent the value +1,279.50:

4892:

Some languages (such as COBOL and PL/I) directly support fixed-point zoned decimal values, assigning an implicit decimal point at some location between the decimal digits of a number.

7406: 6236:

provide Boolean transformations for converting groups of three BCD-encoded digits to and from 10-bit values that can be efficiently encoded in hardware with only 2 or 3 gate delays.

7918:; Rotolo, Louis S.; Wilson, James Bruce (1960). "Part 4. Logical Design of Digital-Computer Circuitry; Chapter 15. Serial Arithmetic Operations; Chapter 15-7. Additional Topics". 9070: 8167: 6924:

Wörterbuch der Elektronik, Datentechnik und Telekommunikation / Dictionary of Electronics, Computing and Telecommunications: Teil 1: Deutsch-Englisch / Part 1: German-English

8695:

data registers, BCD values are packed in an 80-bit format and referred to as decimal integers. In this format, the first 9 bytes hold 18 BCD digits, 2 digits per byte. The

7473:(11 pages) (NB. Besides the combinatorial set of 4-bit BCD "minimum-confusion codes for decimals", of which the author illustrates only one explicitly (here reproduced as 7371:(xii+327+3 pages) (NB. The German edition of volume I was published in 1969, 1971, two editions in 1972, and 1975. Volume II was published in 1970, 1972, 1973, and 1975.) 8995: 8955: 8103: 6321: 8665: 6967: 9452: 7578: 3941:

represents a decimal digit. Packed BCD has been in use since at least the 1960s and is implemented in all IBM mainframe hardware since then. Most implementations are

7477:) in form of a 4-bit graph, the author also shows a 16-state 4-bit "binary code for analog data" in form of a code table, which, however, is not discussed here. The 3882:

Hence the numerical range for one unpacked BCD byte is zero through nine inclusive, whereas the range for one packed BCD byte is zero through ninety-nine inclusive.

8717: 7696: 6336: 5901:

BCD format, typically with two or three digits for the (decimal) exponent. The extra bits of the sign digit may be used to indicate special numeric values, such as

491: 8684:, the BCD values can be unpacked (one BCD digit per byte) or packed (two BCD digits per byte). The value of an unpacked BCD integer is the binary value of the low 230:(NBCD), where each decimal digit is represented by its corresponding four-bit binary value, as shown in the following table. This is also called "8421" encoding. 8618: 7845: 5203:"zone punches" as in the 1400 series. Input/output translation hardware converted between the internal digit pairs and the external standard 6-bit BCD codes. 6638: 6585: 4250:(DPD). The latter has the advantage that subsets of the encoding encode two digits in the optimal seven bits and one digit in four bits, as in regular BCD. 8845: 7919: 5191:

are encoded using digit pairs, with the "zone" in the even-addressed digit and the "digit" in the odd-addressed digit, the "zone" being related to the

4174:

as "FIXED DECIMAL". Beside the IBM System/360 and later compatible mainframes, packed BCD is implemented in the native instruction set of the original

7835: 9125: 3885:

To represent numbers larger than the range of a single byte any number of contiguous bytes may be used. For example, to represent the decimal number

8892: 8367: 8229: 8172: 6197: 214:

formats are still important and continue to be used in financial, commercial, and industrial computing, where the subtle conversion and fractional

9104: 6193: 6623:

Klar, Rainer (1970-02-01). "1.5.3 Konvertierung binär verschlüsselter Dezimalzahlen" [1.5.3 Conversion of binary coded decimal numbers].

6643: 441:, and is the most common encoding. Others include the so-called "4221" and "7421" encoding – named after the weighting used for the bits – and " 9254: 8886:"Signalling Protocols and Switching (SPS) Guidelines for using Abstract Syntax Notation One (ASN.1) in telecommunication application protocols" 8181: 7264: 9020: 7812:

applications. Avoiding the all-zero code pattern allows for loop self-testing and to use the data lines for uninterrupted power distribution.)

3445:−1"), two of the weights are negative. Both ASCII and EBCDIC character codes for the digits, which are examples of zoned BCD, are also shown. 9111: 8853: 8293: 7676: 7637:

Borucki, Lorenz; Dittmann, Joachim (1971) . "2.3 Gebräuchliche Codes in der digitalen Meßtechnik". Written at Krefeld / Karlsruhe, Germany.

7527: 7396: 7280: 7089: 6294:

store the date and time in BCD. This led to a worldwide outage of the console on 1 March 2010. The last two digits of the year stored as BCD

5624: 5579: 5019: 226:

BCD takes advantage of the fact that any one decimal numeral can be represented by a four-bit pattern. An obvious way of encoding digits is

8779: 6680: 5792:

applications, some small processors feature dedicated arithmetic modes, which assist when writing routines that manipulate BCD quantities.

6844: 4929:

The two nibbles of the result, 0001 and 0111, correspond to the digits "1" and "7". This yields "17" in BCD, which is the correct result.

8814: 6287:

handheld computer's manufacturer-supplied software also uses BCD to implement floating point; later Psion models use binary exclusively.

9186: 9157: 7574: 8941:"Non-Access-Stratum (NAS) protocol for 5G System (5GS); Stage 3. (3GPP TS 24.501 version 16.10.0 Release 16) TS 24.501 release 16.10.0" 6932: 6898: 6852: 5783:

This matches much more closely the physical reality of display hardware—a designer might choose to use a series of separate identical

8153:(3 pages) (NB. This paper was prepared for presentation at the AIEE Winter General Meeting, New York, USA, 1956-01-30 to 1956-02-03.) 9318: 9248: 9198: 9177: 8435: 7658: 7364: 7290: 6813: 6781: 6748: 6653: 5929:

programming language, for example, supports five zoned decimal formats, with each one encoding the numeric sign in a different way:

5766: 5748: 5646: 5593: 4969:. The remaining 14 combinations are invalid signs. To illustrate signed BCD subtraction, consider the following problem: 357 − 432. 3846:: Each decimal digit is encoded into one byte, with four bits representing the number and the remaining bits having no significance. 8554: 8205: 7541:(xviii+506 pages) (NB. The French 1967 original book was named "Techniques Booléennes et Calculateurs Arithmétiques", published by 5729: 5686: 5679: 5297:

when the defunct instructions are encountered, so that programs using them can execute without modification on the newer machines.

8723: 6331:

The decision noted that a patent "would wholly pre-empt the mathematical formula and in practical effect would be a patent on the

7978: 7936: 6719: 6676: 6295: 6147:

with swapped nibbles in each byte. Bits, octets and digits indexed from 1, bits from the right, digits and octets from the left.

5701: 7021:

Evans, David Silvester (March 1961). "Chapter Four: Ancillary Equipment: Output-drive and parity-check relays for digitizers".

8980: 8940: 8141: 5838:

involves relatively complex logic that spans digits, and for large numbers, no linear-time conversion algorithm is known (see

8652: 8427: 8315: 8289: 7928: 7876: 5628: 8568: 8340: 7565: 7254: 5871:

Standard BCD requires four bits per digit, roughly 20 per cent more space than a binary encoding (the ratio of 4 bits to log

5708: 8505: 8484: 8411: 5946: 4990:

1001 1000 1011 1111 9 8 11 15 + 0000 0000 0110 0110 0 0 6 6 = 1001 1001 0010 0101 9 9 2 5

4983:

0000 0011 0101 0111 0 3 5 7 + 1001 0101 0110 1000 9 5 6 8 = 1001 1000 1011 1111 9 8 11 15

4179: 172: 6702:

Klar, Rainer (1989) . "1.4 Codes: Binär verschlüsselte Dezimalzahlen" [1.4 Codes: Binary coded decimal numbers].

9442: 9330:

Reversible Implementation of Densely-Packed-Decimal Converter to and from Binary-Coded-Decimal Format Using in IEEE-754R

8593: 8085: 8061: 7885: 7760: 7705: 6548: 6494: 5245:

data type is also implemented, providing machine instructions that perform arithmetic directly on packed decimal data.

5241:

to 8-bit EBCDIC, allowing the addition of many more characters (e.g., lowercase letters). A variable length packed BCD

8035: 7166:), containing all eight states with an even count of 1s, so that inversion of the most-significant bits will create a 5715: 51:

to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional

7826: 3901:

Here, the most significant nibble of the most significant byte has been encoded as zero, so the number is stored as

9457: 8909: 8279: 8185: 7259:. Philips Technical Library (PTL) / Macmillan Education (Reprint of 1st English ed.). Eindhoven, Netherlands: 6711: 6634: 5675: 5617: 7889: 6298:

as 16 causing an error in the unit's date, rendering most functions inoperable. This has been referred to as the

5697: 5585: 5320:

that can be loaded into and stored from the floating point registers, from where computations can be performed.

9447: 9149: 8810: 8681: 7260: 6348: 5329: 4187: 4160: 31: 9313:. Proceedings of the 2006 International Conference on Computer Design (CDES'06). CSREA Press. pp. 64–69. 6217:

applications where 2 or 4 digits after the decimal point are usually enough. Indeed, this is almost a form of

9422: 8696: 8283: 7822: 7032: 6528: 5886: 195: 9095: 8700: 8519: 7607: 7353:

Digitale Elektronik in der Meßtechnik und Datenverarbeitung: Theoretische Grundlagen und Schaltungstechnik

6955: 6507: 6433: 6380: 6359: 6237: 6218: 4246: 4213: 207: 8885: 7158:), containing all eight available binary states with an odd count of 1s, is a slight modification of the 9074: 7356: 7053: 6532: 6276: 5914: 5865: 5823: 5784: 5305: 556: Comment 7028: 6471:

is one of several 2 4 2 1 codes. It is also known as 2* 4 2 1 code.

6429: 6370: 6233: 4240: 7355:. Philips Fachbücher (in German). Vol. I (improved and extended 5th ed.). Hamburg, Germany: 4090:

is, there is always an even number of nibbles because each byte has two of them. Therefore, a word of

9169: 9065: 8109:

Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics

7915: 7205: 7081: 6437: 6353: 6312: 5906: 5788:

system than converting to and from binary. Most pocket calculators do all their calculations in BCD.

5222: 4973: 4972:

In signed BCD, 357 is 0000 0011 0101 0111. The ten's complement of 432 can be obtained by taking the

4163:

exist which avoid the storage penalty and also need no arithmetic operations for common conversions.

194:

is not as widely used as in the past, and is unavailable or limited in newer instruction sets (e.g.,

48: 9273: 6272:

motherboard provided the time encoded in BCD. This form is easily converted into ASCII for display.

5812:

at a decimal digit boundary is simpler. Addition and subtraction in decimal do not require rounding.

9221: 9031: 8712: 8692: 8423: 7194:(May 1969). "II.15. Struktur: Informationsdarstellung im Automaten". Written at Jena, Germany. In 7141: 6417: 6280: 6189: 5910: 5860: 5046: 5042: 5029:

codes that represented numbers, upper-case letters and special characters. Some variation of BCDIC

4937:

to facilitate BCD arithmetic adjustments following binary addition and subtraction operations. The

4197: 4191: 4140: 120: 6804:. Taschenbuch der Nachrichtenverarbeitung (in German). Vol. 2 (3 ed.). Berlin, Germany: 6416:

In a standard packed 4-bit representation, there are 16 states (four bits for each digit) with 10

5722: 8746: 8392: 8332: 8133: 7805: 7733: 7717: 6773: 6524: 6317: 5294: 3953:

C) for positive (+) and 1101 (D) for negative (−). This convention comes from the zone field for

2804: 92: 9269:(Also: ACM SIGPLAN Notices, Vol. 22 #10, IEEE Computer Society Press #87CH2440-6, October 1987) 8768: 8708: 8703:

is contained in the upper half-byte of byte 9. The most significant bit of byte 10 contains the

5868:, requiring binary shifts and adds or the equivalent, per-digit or group of digits is required). 2674: 8803: 7132:

Berger, Erich R. (1962). "1.3.3. Die Codierung von Zahlen". Written at Karlsruhe, Germany. In

9397: 9371: 9341: 9314: 9291:. IEEE Seventh Annual International Phoenix Conference on Computers and Communications, 1988. 9244: 9194: 9173: 9117: 9107: 8849: 8661: 8441: 8431: 8419: 8384: 8288:(x+416+2 pages) (NB. The contents of the book was originally prepared by staff members of the 8246: 8197: 8125: 7958: 7950: 7942: 7932: 7893: 7725: 7672: 7664: 7654: 7542: 7523: 7360: 7308:(270 pages) (NB. This is based on a translation of volume I of the two-volume German edition.) 7276: 7191: 7145: 7133: 7085: 6997: 6979: 6928: 6894: 6848: 6819: 6809: 6797: 6777: 6744: 6715: 6710:]. Sammlung Göschen (in German). Vol. 2050 (4th reworked ed.). Berlin, Germany: 6672: 6649: 6511: 6392: 6299: 6261: 5890: 5317: 3918: 2421: 157: 8839: 7682: 7075: 6624: 6068:, an expansion to BCD where the remaining (unused) bit combinations are used to add specific 5052:

The IBM 1400 series are character-addressable machines, each location being six bits labeled

3852:: Two decimal digits are encoded into a single byte, with one digit in the least significant 9236: 8734: 8376: 8324: 8238: 8189: 8117: 7974: 7709: 7646: 7515: 7432:. The confusion index for decimals using the criterion of "decimal change," is taken to be c 7392: 7286: 7268: 7204:. Elektronisches Rechnen und Regeln (in German). Vol. 5 (1 ed.). Berlin, Germany: 6886: 6375: 6185: 4183: 4087: 3958: 3914: 2739: 164: 6960:

Digitale Rechenanlagen - Grundlagen / Schaltungstechnik / Arbeitsweise / Betriebssicherheit

6244:, except the lead digit, for one of the two alternative decimal encodings specified in the 5300:

Many processors have hardware support for BCD-encoded integer arithmetic. For example, the

464: 8654:

Intel 64 and IA-32 Architectures Software Developer's Manual, Volume 1: Basic Architecture

7966: 7642: 7547: 7511: 7507: 6971: 6882: 6805: 6284: 5894: 5289: 5038: 4966: 4962: 4934: 4147: 2548: 215: 180: 84: 9077: 8620:

Intel 64 and IA-32 Architectures Software Developer's Manual Volume 1: Basic Architecture

6633:]. Sammlung Göschen (in German). Vol. 1241/1241a (1 ed.). Berlin, Germany: 8550: 8274:. Technology Books in Science and Engineering. Vol. 1 (3 ed.). New York, USA: 7927:. McGraw-Hill Electrical and Electronic Engineering Series (1 ed.). New York, USA: 7694:

White, Garland S. (October 1953). "Coded Decimal Number Systems for Digital Computers".

5815:

The alignment of two decimal numbers (for example 1.3 + 27.08) is a simple, exact shift.

4146:

While packed BCD does not make optimal use of storage (using about 20% more memory than

9213: 9162: 7782: 7506:. Translated by Preston, Alan; Summer, Arthur (1st English ed.). Berlin, Germany: 6490: 6425: 6421: 6229: 5898: 5827: 5264: 3473: 2355: 211: 168: 133: 8720:. All decimal integers are exactly representable in double extended-precision format. 7612:

Telefunken-Zeitung (TZ) - Technisch-Wissenschaftliche Mitteilungen der Telefunken GMBH

7195: 4916:

values (since 2 = 16), but only 10 values are valid (0000 through 1001). For example:

9436: 9193:(1 (reprint) ed.). Malabar, Florida, USA: Robert E. Krieger Publishing Company. 8396: 8227:

Lippel, Bernhard (December 1955). "A Decimal Code for Analog-to-Digital Conversion".

8003: 7801: 7167: 6386: 6291: 6245: 5839: 5835: 3910: 3857: 1979: 1114: 1048: 129: 76: 8869: 8804:"Decimal CORDIC Rotation based on Selection by Rounding: Algorithm and Architecture" 8336: 8137: 7737: 5818:

Conversion to a character form or for display (e.g., to a text-based format such as

4945:

and the CPUs of the x86 family provide the opcode DAA (Decimal Adjust Accumulator).

3921:

are used to convert a numeral to its equivalent bit pattern or reverse the process.

17: 8738: 6802:

Taschenbuch der Informatik - Band II - Struktur und Programmierung von EDV-Systemen

6560: 6552: 5332:) computes an unsigned 8-digit packed BCD addition using 32-bit binary operations: 5101: 5025: 4961:. To represent the sign of a number in BCD, the number 0000 is used to represent a 4098:)−1 decimal digits, which is always an odd number of digits. A decimal number with 3898:

Decimal: 0 1 2 3 4 5 Binary : 0000 0001 0010 0011 0100 0101

140: 44: 9345: 9311:

Modified Carry Look Ahead BCD Adder With CMOS and Reversible Logic Implementation

8572: 8310: 7871: 7501: 7296: 7199: 7022: 6922: 6876: 6838: 6480:

The Jump-at-8 code is also known as unsymmetrical 2 4 2 1 code.

5885:

Various BCD implementations exist that employ other representations for numbers.

5175:

The memory of the IBM 1620 is organized into 6-bit addressable digits, the usual

4980:

Now that both numbers are represented in signed BCD, they can be added together:

106:

BCD usually implies a full byte for each digit (often including a sign), whereas

9401: 7519: 6241: 6222: 5664: 5606: 3950: 2230: 2044: 64: 52: 8363:"Arithmetic Operations for Digital Computers Using a Modified Reflected Binary" 8362: 7931:(printer: The Maple Press Company, York, Pennsylvania, USA). pp. 517–518. 7713: 6704:

Digitale Rechenautomaten – Eine Einführung in die Struktur von Computerhardware

9375: 9217: 8533: 7962: 7840: 7650: 7619: 7272: 7057: 7049: 6890: 6468: 5256:, packed BCD is supported in software by IBM's Commercial Subroutine Package. 5234: 4954: 4938: 4133: 3942: 3892: 3482: 3051: 982: 8586: 8388: 8380: 8250: 8242: 8201: 8193: 8129: 8121: 7946: 7897: 7752: 7729: 7721: 7024:

Digital Data: Their derivation and reduction for analysis and process control

4926:

10001 + 0110 = 00010111 => 0001 0111 17 + 6 = 23 1 7

4128:

0001 0010 0011 0100 0101 0110 0111 1101 1 2 3 4 5 6 7 −

3839:, it is possible to use one of the following methods to encode a BCD number: 9328:

Kaivani, A.; Alhosseini, A. Zaker; Gorgin, S.; Fazlali, M. (December 2006).

8328: 8082:

Some Recently Developed Digital Devices for Encoding the Rotations of Shafts

7809: 7610:(ed.). "Ermittlung des Codes und der logischen Schaltung einer Zähldekade". 6332: 6283:

processor has a BCD mode for the addition and subtraction instructions. The

6269: 6069: 5272: 4942: 4880: 203: 128:

typically needed to hold them is also known as a tetrade) while the unused,

60: 8027: 7970: 6708:

Digital Computers – An Introduction into the structure of computer hardware

3860:) and the other numeral in the most significant nibble (bits 4 through 7). 39: 9206: 8704: 8005:(xxiv+835+1 pages) (NB. Ledley classified the described cyclic code as a 6547:

In a similar fashion, multiple characters were often packed into machine

5902: 5809: 5253: 5249: 5215: 5211: 5207: 5034: 4912: 3870:

using unpacked BCD results in the following binary pattern of two bytes:

3538: 3532: 3477: 3417:

digits from 0 to 9 in various BCD encoding systems. In the headers, the "

442: 112: 9240: 8916: 8058:

A Cyclic Progressive Binary-coded-decimal System of Representing Numbers

7532:. License No. 202-100/542/73. Order No. 7617470(6047) ES 19 B 1 / 20 K 3 6671:(205 pages) (NB. A 2019 reprint of the first edition is available under 218:

that are inherent in binary floating point formats cannot be tolerated.

91:, usually four or eight. Sometimes, special bit patterns are used for a 8769:"A Cordic-based Architecture for High Performance Decimal Calculations" 6365: 5631: in this section. Unsourced material may be challenged and removed. 5260: 5084:

are zero and the digit value represented by standard 4-bit BCD in bits

4958: 4155: 3526: 3520: 3414: 80: 8116:(2). Bell Telephone Laboratories, Whippany, New Jersey, USA: 120–122. 5846:

and calculating such values. This is useful in financial calculations.

5100:

are derived simply from the "12", "11", and "0" "zone punches" in the

8685: 7402: 6556: 6325: 6265: 5952: 5268: 3954: 3938: 3853: 3565: 125: 9332:. 9th International Conference on Information Technology (ICIT'06). 7500:

Chinal, Jean P. (January 1973). "Codes". Written at Paris, France.

7208:. p. 161. License no. 202-100/416/69. Order no. 4666 ES 20 K 3. 4143:

integer can represent values from −2,147,483,648 to +2,147,483,647.

3433:" indicates the weight of each bit. In the fifth column ("BCD 8 167:, and is implemented in the instruction set of machines such as the 7606:

Stopper, Herbert (March 1960). Written at Litzelstetten, Germany.

9427: 9287:

Shirazi, Behrooz; Yun, David Y. Y.; Zhang, Chang N. (March 1988).

8068:

A Cyclic-Coded Binary-Coded-Decimal System of Representing Numbers

7001: 6592: 5926: 5313: 5012: 4167: 4151: 3558: 184: 38: 7668: 7395:(June 1954). "IV. Examples A. Binary Codes for Decimals, n = 4". 5840:

Binary number § Conversion to and from other numeral systems

9333: 9292: 9121: 8991: 8987: 8951: 8947: 8775: 8707:(0 = positive and 1 = negative; bits 0 through 6 of byte 10 are 8534:"IBM 1401/1440/1460/1410/7010 Character Code Chart in BCD Order" 8445: 7954: 7149: 6983: 6823: 6257: 6073: 6061: 5301: 4171: 3917:

operations are used to pack or unpack a packed BCD digit. Other

3836: 99: 9205:(NB. At least some batches of the Krieger reprint edition were 6964:

Digital computers - Basics / Circuits / Operation / Reliability

6726:

Die nicht erlaubten 0/1-Muster nennt man auch Pseudodezimalen.

5259:

Today, BCD data is still heavily used in IBM databases such as

3873:

Decimal: 9 1 Binary : 0000 1001 0000 0001

9409: 9383: 9346:"Bibliography of material on Decimal Arithmetic – by category" 8689: 8465: 8168:"Unit-Distance Binary-Decimal Codes for Two-Track Commutation" 7201:

Digitale Automaten – Theorie, Struktur, Technik, Programmieren

6975: 5925:

Signed decimal values may be represented in several ways. The

5819: 5658: 5600: 5559: 5309: 5285: 4259: 4175: 199: 176: 88: 9423:

Convert BCD to decimal, binary and hexadecimal and vice versa

8276:

Technology Press of the Massachusetts Institute of Technology

7198:; Kämmerer, Wilhelm; Schröder, Kurz; Winkler, Helmut (eds.). 6743:(in German) (2 ed.). R. Oldenbourg Verlag München Wien. 4879:

Note: These characters vary depending on the local character

3876:

In packed BCD, the same number would fit into a single byte:

118:

The ten states representing a BCD digit are sometimes called

6328:

for converting BCD-encoded numbers to binary on a computer.

5826:) is a simple per-digit mapping, and can be done in linear ( 8871:

3GPP TS 29.002: Mobile Application Part (MAP) specification

7872:"Can You Take Advantage of the Cyclic Binary-Decimal Code?" 6335:

itself". This was a landmark judgement that determined the

5132:, and a "0 zone" (a 0 punch combined with any others) set 4953:

Subtraction is done by adding the ten's complement of the

8104:"Cyclic Decimal Codes for Analogue to Digital Converters" 7140:(in German) (1 ed.). Berlin / Göttingen / New York: 4994:

925 is 1000 − 925 = 75, so the calculated answer is −75.

102:-oriented systems (i.e. most modern computers), the term 9309:

Thapliyal, Himanshu; Arabnia, Hamid R. (November 2006).

9289:

VLSI designs for redundant binary-coded decimal addition

8874:(Technical report). 2013. sec. 17.7.8 Common data types. 7641:(in German) (2 ed.). Berlin / Heidelberg, Germany: 7632: 7630: 6240:(DPD) is a similar scheme that is used for most of the 30:"BCD code" redirects here. For BCD character sets, see 8699:

is contained in the lower half-byte of byte 0 and the

8664:. 2020-05-27 . pp. 3–2, 4-9–4-11 . 253665-072US. 8021: 8019: 8017: 8015: 7888:, a division of Dun-Donnelley Publishing Corporation, 6134:

Used as filler when there is an odd number of digits

467: 7804:

only in the encoding of state 0 to make it a cyclic

7567:

Military Handbook: Encoders - Shaft Angle To Digital

7481:

shown here is a modification of code I discussed by

6800:; Weber, Wolfgang; Heinemann, Traute, eds. (1974) . 8711:bits). Negative decimal integers are not stored in 8097: 8095: 6389:, an algorithm for converting binary numbers to BCD 5033:is used in most early IBM computers, including the 458: 454: 450: 446: 9161: 8910:"XOM Mobile Application Part (XMAP) Specification" 7253:Dokter, Folkert; Steinhauer, Jürgen (1973-06-18). 7127: 7125: 7123: 7121: 6412: 6410: 6408: 6072:characters, with digits similar to those found in 485: 8496: 8494: 7119: 7117: 7115: 7113: 7111: 7109: 7107: 7105: 7103: 7101: 6424:, whereas in more densely packed schemes such as 6279:use a BCD format for floating point numbers. The 5994:Sign nibble in the first (most significant) byte 5974:Sign nibble in the last (least significant) byte 9222:"Superoptimizer: A look at the smallest program" 8265: 8263: 8261: 8161: 8159: 7785:[Continuous loop code]. 1.02 (in German) 7186: 7184: 7182: 7180: 7178: 7176: 6837:Tietze, Ulrich; Schenk, Christoph (2012-12-06). 9103:. The Systems Programming Series (1 ed.). 8718:double-extended-precision floating-point format 8080:Petherick, Edward John; Hopkins, A. J. (1958). 7697:Proceedings of the Institute of Radio Engineers 7601: 7599: 7593:(NB. Supersedes MIL-HDBK-231(AS) (1970-07-01).) 7346: 7344: 7342: 7340: 7338: 7336: 7334: 7248: 7246: 7244: 7242: 7240: 7238: 7236: 6543: 6541: 5859:Some operations are more complex to implement. 95:or other indications (e.g. error or overflow). 9402:"A Summary of Densely Packed Decimal encoding" 7910: 7908: 7495: 7493: 7491: 7332: 7330: 7328: 7326: 7324: 7322: 7320: 7318: 7316: 7314: 7234: 7232: 7230: 7228: 7226: 7224: 7222: 7220: 7218: 7216: 6770:Introduction to digital information processing 5156:in the punched card, was encoded in memory as 5023:(BCDIC, sometimes just called BCD), for 6-bit 9097:Coded Character Sets, History and Development 8272:Notes on Analog-Digital Conversion Techniques 7398:Optimized Data Encoding for Digital Computers 7387: 7385: 7383: 7381: 7379: 7377: 7351:Dokter, Folkert; Steinhauer, Jürgen (1975) . 7060:of the resulting 5-bit code is also known as 6927:. Vol. 1 (2 ed.). Springer-Verlag. 4190:line of mainframes (descended from the 1950s 4186:mainframes, and is the native format for the 8: 9376:"A Summary of Chen-Ho Decimal Data encoding" 8304: 8302: 7795: 6766:Einführung in die digitale Datenverarbeitung 6741:Lexikon der Informatik und Datenverarbeitung 6264:stores the date and time in BCD because the 8846:Tata McGraw-Hill Publishing Company Limited 7560: 7558: 7210:(NB. A second edition 1973 exists as well.) 6697: 6695: 6693: 6618: 6616: 6514:code or Watts reflected decimal (WRD) code. 5594:Learn how and when to remove these messages 3895:format, a program would encode as follows: 3879:Decimal: 9 1 Binary : 1001 0001 3864:As an example, encoding the decimal number 156:BCD's main virtue, in comparison to binary 9146:Arithmetic Operations in Digital Computers 8311:"A New Representation for Decimal Numbers" 8286:pp. 3-7–3-8 , 3-10–3-16 , 6-65–6-60 . 6626:Digitale Rechenautomaten – Eine Einführung 6454: 6452: 6450: 6448: 6446: 6440:in 1024 states (10 bits for three digits). 6268:real-time clock chip used in the original 4150:to store the same numbers), conversion to 3835:As most computers deal with data in 8-bit 9168:(1 ed.). Binghamton, New York, USA: 7836:Bell Telephone Laboratories, Incorporated 5767:Learn how and when to remove this message 5749:Learn how and when to remove this message 5647:Learn how and when to remove this message 466: 8368:IRE Transactions on Electronic Computers 8292:, Department of Electrical Engineering, 8230:IRE Transactions on Electronic Computers 8188:, Philadelphia, Pennsylvania, USA: 139. 8173:IRE Transactions on Electronic Computers 8084:(Technical Note MS21). Farnborough, UK: 8066:(4 pages) (NB. Sometimes referred to as 8060:(Technical Note MS15). Farnborough, UK: 7921:Digital Computer and Control Engineering 7800:(English: "loop code"). It differs from 6436:encodings there are fewer—e.g., only 24 6337:patentability of software and algorithms 6078: 5931: 4919:1001 + 1000 = 10001 9 + 8 = 17 4281: 3967: 3447: 495: 232: 9453:Non-standard positional numeral systems 9105:Addison-Wesley Publishing Company, Inc. 8166:Tompkins, Howard E. (September 1956) . 8056:Petherick, Edward John (October 1953). 7138:Taschenbuch der Nachrichtenverarbeitung 6576: 6404: 5144:in the punched card format, is encoded 429:This scheme can also be referred to as 8462:IBM System/370 Principles of Operation 8182:Moore School of Electrical Engineering 7759:. 2019-05-01 . Section 2.4 5211 Code. 7482: 6639:G. J. Göschen'sche Verlagsbuchhandlung 5685:Please improve this section by adding 5382:// unsigned 32-bit intermediate values 4154:, EBCDIC, or the various encodings of 453:in 4221 (two encodings are possible), 9021:"Timer Counter Circuits in an IBM PC" 8416:Microprocessors - A Programmer's View 7159: 6845:Springer Science & Business Media 6057:Telephony binary-coded decimal (TBCD) 5318:unique 18-digit (ten-byte) BCD format 5221:are encoded using digit pairs (using 5020:Binary-Coded Decimal Interchange Code 4278:EBCDIC zoned decimal conversion table 1241:Jump-at-8 (2 4 2 1) 1179:Jump-at-2 (2 4 2 1) 238: 235: 7: 7783:"Unterbrechungsfreier Schleifencode" 7639:Digitale Meßtechnik: Eine Einführung 6684: 6143:The mentioned 3GPP document defines 5629:adding citations to reliable sources 5120:punches. A "12 zone" punch set both 497:4-bit BCD codes and pseudo-tetrades 87:is represented by a fixed number of 27:System of digitally encoding numbers 9229:ACM SIGOPS Operating Systems Review 8651:"4.7 BCD and packed BCD integers". 8460:"Chapter 8: Decimal Instructions". 7870:Glixon, Harry Robert (March 1957). 7575:United States Department of Defense 7438:Minimum-confusion code for decimals 7265:N. V. Philips' Gloeilampenfabrieken 7077:Principles of Modern Digital Design 6631:Digital Computers – An Introduction 6188:to send dialed numbers, as well as 5806:Scaling by a power of 10 is simple. 4898:F1 F2 F7 F9 F5 C0 1 2 7 9. 5 +0 8680:When operating on BCD integers in 8626:. Intel. March 2013. Section 4.7. 8479:"Chapter 3: Data Representation". 8361:Lucal, Harold M. (December 1959). 8309:Yuen, Chun-Kwong (December 1977). 7503:Design Methods for Digital Systems 6903:. 9783642876639, 978-3-642-87664-6 5284:The Digital Equipment Corporation 4998:0002 would have to be calculated. 4965:, and 1001 is used to represent a 4258:Some implementations, for example 25: 9144:Richards, Richard Kohler (1955). 9131:from the original on May 26, 2016 7794:(NB. The author called this code 7781:Paul, Matthias R. (1995-08-10) . 7753:"Different Types of Binary Codes" 6921:Ferretti, Vittorio (2013-03-13). 5575:This section has multiple issues. 5092:. For most other characters bits 1674:White (5 2 1 1) 457:in 7421, while in Excess-3 it is 445:". For example, the BCD digit 6, 8898:from the original on 2013-12-04. 8749:, Department of Computer Science 8557:from the original on 2018-05-08. 8102:O'Brien, Joseph A. (May 1956) . 8007:cyclic decimal-coded binary code 6966:] (in German) (2 ed.). 5897:, and others typically employ a 5663: 5605: 5564: 5421:// sum without carry propagation 4086:No matter how many bytes wide a 2929:6 3 −2 −1 (II) 859:8 4 2 1 (XS-0) 9260:from the original on 2017-07-04 9001:from the original on 2022-02-26 8961:from the original on 2022-02-17 8841:Introduction to Microprocessors 8820:from the original on 2022-10-09 8785:from the original on 2010-01-05 8671:from the original on 2020-08-06 8633:from the original on 2013-04-02 8599:from the original on 2023-11-20 8343:from the original on 2020-08-08 8038:from the original on 2018-07-16 7990:from the original on 2021-02-19 7851:from the original on 2020-08-05 7763:from the original on 2020-05-18 7584:from the original on 2020-07-25 7409:from the original on 2020-07-03 6739:Schneider, Hans-Jochen (1986). 6662:from the original on 2020-04-18 6602:from the original on 2022-10-09 6324:'s decision that had allowed a 5616:needs additional citations for 5583:or discuss these issues on the 5187:, an odd parity check bit. BCD 4201:corresponding positive number. 4166:Packed BCD is supported in the 3413:The following table represents 2868:6 3 −2 −1 (I) 9209:with defective pages 115–146.) 9094:Mackenzie, Charles E. (1980). 8428:McGraw-Hill Publishing Company 8412:Dewar, Robert Berriedale Keith 8316:IEEE Transactions on Computers 7929:McGraw-Hill Book Company, Inc. 6875:Kowalski, Emil (2013-03-08) . 6184:This format is used in modern 6034:Separate sign character byte ( 6010:Separate sign character byte ( 5834:)) time. Conversion from pure 5060:plus an odd parity check bit ( 1367:4 2 2 1 (II) 1: 9302:Fundamentals of Digital Logic 8587:"The 68000's Instruction Set" 8506:Digital Equipment Corporation 8485:Digital Equipment Corporation 8140:. Paper 56-21. Archived from 7577:. 1991-09-30. MIL-HDBK-231A. 7478: 7155: 5687:secondary or tertiary sources 4180:Digital Equipment Corporation 4139:In contrast, a 4-byte binary 1304:4 2 2 1 (I) 173:Digital Equipment Corporation 8915:. p. 93. Archived from 8745:. Iowa City, Iowa, USA: The 8739:"BCD Arithmetic, a tutorial" 8660:. Version 072. Vol. 1. 8502:VAX-11 Architecture Handbook 8481:PDP-11 Architecture Handbook 8290:Servomechanisms Laboraratory 8086:Royal Aircraft Establishment 8062:Royal Aircraft Establishment 8026:Savard, John J. G. (2018) . 7886:Technical Publishing Company 7706:Institute of Radio Engineers 7044:(8+82 pages) (NB. The 4-bit 7002:"General Decimal Arithmetic" 6840:Advanced Electronic Circuits 6495:Royal Aircraft Establishment 6042:) preceding the digit bytes 6018:) following the digit bytes 5822:, or to drive signals for a 5463:// all the binary carry bits 5316:x86 architecture supports a 5206:In the decimal architecture 4122:+1) bytes of storage space. 171:series and its descendants, 8280:John Wiley & Sons, Inc. 7520:10.1007/978-3-642-86187-1_3 7154:(NB. The shown Kautz code ( 6772:] (in German). Munich: 6712:Walter de Gruyter & Co. 6635:Walter de Gruyter & Co. 5881:Representational variations 5796:Comparison with pure binary 4923:is treated as two nibbles: 4262:mainframe systems, support 2990:8 4 −2 −1 985:(2 4 2 1) 431:Simple Binary-Coded Decimal 163:BCD was used in many early 9474: 9406:General Decimal Arithmetic 9380:General Decimal Arithmetic 9350:General Decimal Arithmetic 8838:Mathur, Aditya P. (1989). 8414:; Smosna, Matthew (1990). 8186:University of Pennsylvania 7983:. . ark:/13960/t72v3b312. 7890:Dun & Bradstreet Corp. 7714:10.1109/JRPROC.1953.274330 7474: 7437: 7420: 7163: 7027:(1 ed.). London, UK: 6683:. A reworked and expanded 6586:"ia32 architecture manual" 6221:since the position of the 5487:// just the BCD carry bits 5010: 4911:It is possible to perform 4209:Fixed-point packed decimal 4094:bytes can contain up to (2 3352: 3291: 3230: 3169: 3108: 3045: 2984: 2923: 2862: 2797: 2732: 2667: 2606: 2541: 2480: 2414: 2348: 2287: 2224: 2163: 2102: 2037: 1972: 1911: 1850: 1791: 1730: 1667: 1606: 1545: 1484: 1423: 1360: 1297: 1234: 1173: 1107: 1041: 975: 914: 853: 789: 29: 8682:general-purpose registers 8028:"Decimal Representations" 7808:for full-circle rotatory 7651:10.1007/978-3-642-80560-8 7273:10.1007/978-1-349-01417-0 7045: 6891:10.1007/978-3-642-87663-9 6764:Tafel, Hans Jörg (1971). 6248:floating-point standard. 6007:Signed trailing separate 5237:, IBM expanded 6-bit BCD 5233:With the introduction of 5183:, used as a flag bit and 5104:character code, and bits 4888:Fixed-point zoned decimal 4290: 4287: 3356: 3295: 3234: 3173: 3112: 3049: 2988: 2927: 2866: 2801: 2736: 2671: 2610: 2545: 2484: 2418: 2352: 2291: 2228: 2169:4 3 1 1 2167: 2106: 2041: 1976: 1915: 1854: 1795: 1736:5 2 1 1 1734: 1671: 1612:5 3 1 1 1610: 1551:5 1 2 1 1549: 1490:5 2 2 1 1488: 1429:5 4 2 1 1427: 1364: 1301: 1238: 1177: 1111: 1045: 979: 920:7 4 2 1 918: 857: 793: 614: 9300:Brown; Vranesic (2003). 8811:British Computer Society 8767:University of Alicante. 8381:10.1109/TEC.1959.5222057 8284:Chapman & Hall, Ltd. 8243:10.1109/TEC.1955.5219487 8194:10.1109/TEC.1956.5219934 8122:10.1109/TCE.1956.6372498 7828:Pulse Code Communication 7618:(127). Berlin, Germany: 7261:The Macmillan Press Ltd. 6714:pp. 25, 28, 38–39. 6658:. . Archiv-Nr. 7990709. 6349:Bi-quinary coded decimal 6031:Signed leading separate 5887:Programmable calculators 5334: 5164:, represented by a lone 4233:Higher-density encodings 4188:Burroughs Medium Systems 32:BCD (character encoding) 8697:least-significant digit 8329:10.1109/TC.1977.1674792 7074:Lala, Parag K. (2007). 7048:BCD code with an extra 7033:Interscience Publishers 6970:, Zürich, Switzerland: 6956:Speiser, Ambrosius Paul 5263:and processors such as 5168:punch in the card, and 5068:). For encoding digits 5064:) and a word mark bit ( 4182:and some models of the 4072:1 1 1 1 4056:1 1 1 0 4040:1 1 0 1 4024:1 1 0 0 4008:1 0 1 1 3992:1 0 1 0 3978:8 4 2 1 8701:most-significant digit 8551:"6502 Instruction Set" 7796: 7029:Hilger & Watts Ltd 6381:Densely packed decimal 6360:Binary integer decimal 6238:Densely packed decimal 6219:fixed point arithmetic 6171: 5917:(a blinking display). 5785:seven-segment displays 5698:"Binary-coded decimal" 5674:relies excessively on 5148:. The currency symbol 5037:(introduced in 1959), 4247:densely packed decimal 4192:Electrodata 200 series 487: 56: 9170:John Wiley & Sons 7916:Ledley, Robert Steven 7844:. Serial No. 785697. 7841:U.S. patent 2,632,058 7357:Deutsche Philips GmbH 7082:John Wiley & Sons 7054:least significant bit 6277:Atari 8-bit computers 6204:Alternative encodings 6149: 5866:binary multiplication 5824:seven-segment display 5306:Motorola 68000 series 3891:in packed BCD, using 488: 486:{\displaystyle 6+3=9} 449:in 8421 notation, is 151:pseudo-decimal digits 42: 9274:"GNU Superoptimizer" 9066:Gottschalk v. Benson 8743:Arithmetic Tutorials 7608:Runge, Wilhelm Tolmé 7206:Akademie-Verlag GmbH 6354:Binary-coded ternary 6313:Gottschalk v. Benson 6290:Early models of the 5780:single sub-circuit. 5625:improve this article 5547:// corrected BCD sum 5223:two-out-of-five code 5043:decimal architecture 465: 206:). However, decimal 187:-series processors. 69:binary-coded decimal 18:Binary coded decimal 9443:Computer arithmetic 9336:. pp. 273–276. 9241:10.1145/36204.36194 9191:Decimal Computation 9164:Decimal Computation 8569:"NMOS 6502 Opcodes" 8520:"ILE RPG Reference" 8424:New York University 7877:Control Engineering 7645:. pp. 10–23 . 7256:Digital Electronics 7142:Springer-Verlag OHG 6878:Nuclear Electronics 6648:. pp. 17, 21. 6508:O'Brien code type I 6296:were misinterpreted 6281:MOS Technology 6502 6161:bits 4321 of octet 6151:bits 8765 of octet 5128:, an "11 zone" set 5047:IBM 700/7000 series 5017:IBM used the terms 4902:Operations with BCD 3957:characters and the 498: 183:, and the Motorola 83:numbers where each 9398:Cowlishaw, Mike F. 9372:Cowlishaw, Mike F. 9342:Cowlishaw, Mike F. 8747:University of Iowa 8176:. Correspondence. 7806:unit-distance code 7708:(IRE): 1450–1452. 7144:. pp. 68–75. 7134:Steinbuch, Karl W. 7084:. pp. 20–25. 6998:Cowlishaw, Mike F. 6798:Steinbuch, Karl W. 6774:Carl Hanser Verlag 6525:Excess-3 Gray code 6318:U.S. Supreme Court 6262:personal computers 5970:(canonical format) 5556:BCD in electronics 5442:// provisional sum 5295:exception handling 5136:. Thus the letter 3919:bitwise operations 1856:Magnetic tape 496: 483: 158:positional systems 132:-states are named 57: 9458:Binary arithmetic 9295:. pp. 52–56. 9148:. New York, USA: 9113:978-0-201-14460-4 9028:www.se.ecu.edu.au 8855:978-0-07-460222-5 8735:Jones, Douglas W. 8716:converted to the 8662:Intel Corporation 8450:(xviii+462 pages) 8426:, New York, USA: 8420:Courant Institute 8323:(12): 1286–1288. 7834:. New York, USA: 7681:(viii+252 pages) 7677:978-3-642-80561-5 7529:978-0-387-05871-9 7405:pp. 47–57 . 7393:Kautz, William H. 7282:978-1-349-01419-4 7192:Kämmerer, Wilhelm 7091:978-0-470-07296-7 7035:. pp. 46–64 6527:is also known as 6510:is also known as 6493:is also known as 6393:Year 2000 problem 6310:In the 1972 case 6300:Year 2010 problem 6285:Psion Organiser 1 6234:Chen–Ho encodings 6165:encoding digit 2( 6141: 6140: 6076:original design. 6074:telephone keypads 6054: 6053: 5921:Signed variations 5891:Texas Instruments 5777: 5776: 5769: 5759: 5758: 5751: 5733: 5657: 5656: 5649: 5598: 4974:nine's complement 4875: 4874: 4291:EBCDIC character 4274:F1 F2 D3 1 2 −3 4084: 4083: 3833: 3832: 3411: 3410: 427: 426: 165:decimal computers 135:pseudo-tetrad(e)s 16:(Redirected from 9465: 9419: 9417: 9416: 9393: 9391: 9390: 9360: 9358: 9357: 9337: 9324: 9305: 9296: 9281: 9268: 9266: 9265: 9259: 9226: 9216:(October 1987). 9204: 9183: 9167: 9153: 9152:. pp. 397–. 9140: 9138: 9136: 9130: 9102: 9081: 9062: 9056: 9055:MC6818 datasheet 9053: 9047: 9045: 9043: 9042: 9036: 9030:. Archived from 9025: 9017: 9011: 9009: 9007: 9006: 9000: 8985: 8977: 8971: 8969: 8967: 8966: 8960: 8945: 8937: 8931: 8930: 8928: 8927: 8921: 8914: 8906: 8900: 8899: 8897: 8890: 8882: 8876: 8875: 8866: 8860: 8859: 8835: 8829: 8828: 8826: 8825: 8819: 8808: 8800: 8794: 8793: 8791: 8790: 8784: 8773: 8764: 8758: 8757: 8755: 8754: 8731: 8725: 8722: 8713:two's complement 8678:. p. 4-10: 8677: 8676: 8670: 8659: 8648: 8642: 8641: 8639: 8638: 8632: 8625: 8615: 8609: 8607: 8605: 8604: 8598: 8591: 8583: 8577: 8576: 8571:. Archived from 8565: 8559: 8558: 8547: 8541: 8540: 8538: 8530: 8524: 8523: 8516: 8510: 8509: 8498: 8489: 8488: 8476: 8470: 8469: 8457: 8451: 8449: 8408: 8402: 8400: 8358: 8352: 8351: 8349: 8348: 8306: 8297: 8287: 8267: 8256: 8254: 8224: 8218: 8216: 8214: 8213: 8204:. Archived from 8163: 8154: 8152: 8150: 8149: 8099: 8090: 8089: 8077: 8071: 8065: 8053: 8047: 8046: 8044: 8043: 8023: 8010: 8002: 7996: 7995: 7989: 7926: 7912: 7903: 7901: 7867: 7861: 7859: 7857: 7856: 7850: 7843: 7833: 7819: 7813: 7799: 7793: 7791: 7790: 7778: 7772: 7771: 7769: 7768: 7749: 7743: 7741: 7691: 7685: 7680: 7634: 7625: 7623: 7603: 7594: 7592: 7590: 7589: 7583: 7572: 7562: 7553: 7551: 7540: 7538: 7537: 7497: 7486: 7450: 7424:of Sec. II for Δ 7415: 7414: 7389: 7372: 7370: 7348: 7309: 7307: 7305: 7304: 7295:. Archived from 7250: 7211: 7209: 7188: 7171: 7153: 7129: 7096: 7095: 7071: 7065: 7043: 7041: 7040: 7018: 7012: 7011: 7009: 7008: 6994: 6988: 6987: 6952: 6946: 6945: 6943: 6942: 6918: 6912: 6911: 6909: 6908: 6872: 6866: 6865: 6863: 6862: 6834: 6828: 6827: 6794: 6788: 6787: 6761: 6755: 6754: 6736: 6730: 6728: 6699: 6688: 6687:exists as well.) 6681:978-3-11002793-8 6670: 6668: 6667: 6647: 6620: 6611: 6610: 6608: 6607: 6601: 6590: 6581: 6564: 6545: 6536: 6521: 6515: 6504: 6498: 6487: 6481: 6478: 6472: 6465: 6459: 6456: 6441: 6414: 6376:Decimal computer 6371:Chen–Ho encoding 6212: 6186:mobile telephony 6180: 6176: 6155:encoding digit 2 6079: 6050: 6041: 6037: 6026: 6017: 6013: 6002: 5983: 5968:Signed trailing 5963: 5932: 5889:manufactured by 5772: 5765: 5754: 5747: 5743: 5740: 5734: 5732: 5691: 5667: 5659: 5652: 5645: 5641: 5638: 5632: 5609: 5601: 5590: 5568: 5567: 5560: 5551: 5548: 5545: 5542: 5539: 5536: 5533: 5530: 5527: 5524: 5521: 5518: 5515: 5512: 5509: 5506: 5503: 5500: 5497: 5494: 5491: 5488: 5485: 5482: 5479: 5476: 5473: 5470: 5467: 5464: 5461: 5458: 5455: 5452: 5449: 5446: 5443: 5440: 5437: 5434: 5431: 5428: 5425: 5422: 5419: 5416: 5413: 5410: 5407: 5404: 5401: 5398: 5395: 5392: 5389: 5386: 5383: 5380: 5377: 5374: 5371: 5368: 5365: 5362: 5359: 5356: 5353: 5350: 5347: 5344: 5341: 5338: 5288:series includes 5172:in core memory. 5002:BCD in computers 4282: 4241:Chen–Ho encoding 4198:Ten's complement 4184:SDS Sigma series 4178:processors from 4141:two's complement 4136:of the machine. 4117: 4115: 4114: 4111: 4108: 4102:digits requires 3968: 3961:representation. 3959:signed overpunch 3906: 3890: 3869: 3858:bits 0 through 3 3554: 3550: 3546: 3541: 3536: 3530: 3524: 3515: 3511: 3507: 3498: 3494: 3490: 3469: 3465: 3461: 3448: 3444: 3440: 3436: 3432: 3430: 3426: 3422: 2807: 2742: 2677: 2551: 2425: 2359: 2047: 1982: 1675: 1369: 1306: 1243: 1118: 1052: 986: 499: 492: 490: 489: 484: 460: 456: 452: 448: 233: 144: 75:) is a class of 21: 9473: 9472: 9468: 9467: 9466: 9464: 9463: 9462: 9448:Numeral systems 9433: 9432: 9414: 9412: 9396: 9388: 9386: 9370: 9367: 9355: 9353: 9340: 9327: 9321: 9308: 9299: 9286: 9272: 9263: 9261: 9257: 9251: 9224: 9214:Massalin, Henry 9212: 9201: 9187:Schmid, Hermann 9185: 9180: 9158:Schmid, Hermann 9156: 9143: 9134: 9132: 9128: 9114: 9100: 9093: 9090: 9088:Further reading 9085: 9084: 9063: 9059: 9054: 9050: 9040: 9038: 9034: 9023: 9019: 9018: 9014: 9004: 9002: 8998: 8983: 8979: 8978: 8974: 8964: 8962: 8958: 8943: 8939: 8938: 8934: 8925: 8923: 8919: 8912: 8908: 8907: 8903: 8895: 8888: 8884: 8883: 8879: 8868: 8867: 8863: 8856: 8837: 8836: 8832: 8823: 8821: 8817: 8806: 8802: 8801: 8797: 8788: 8786: 8782: 8771: 8766: 8765: 8761: 8752: 8750: 8737:(2015-11-25) . 8733: 8732: 8728: 8674: 8672: 8668: 8657: 8650: 8649: 8645: 8636: 8634: 8630: 8623: 8617: 8616: 8612: 8602: 8600: 8596: 8589: 8585: 8584: 8580: 8567: 8566: 8562: 8549: 8548: 8544: 8536: 8532: 8531: 8527: 8518: 8517: 8513: 8500: 8499: 8492: 8478: 8477: 8473: 8459: 8458: 8454: 8438: 8410: 8409: 8405: 8360: 8359: 8355: 8346: 8344: 8308: 8307: 8300: 8269: 8268: 8259: 8226: 8225: 8221: 8211: 8209: 8165: 8164: 8157: 8147: 8145: 8101: 8100: 8093: 8079: 8078: 8074: 8055: 8054: 8050: 8041: 8039: 8025: 8024: 8013: 7997:. p. 517: 7993: 7991: 7987: 7981: 7939: 7924: 7914: 7913: 7906: 7869: 7868: 7864: 7854: 7852: 7848: 7839: 7831: 7825:(1953-03-17) . 7821: 7820: 7816: 7788: 7786: 7780: 7779: 7775: 7766: 7764: 7751: 7750: 7746: 7693: 7692: 7688: 7661: 7643:Springer-Verlag 7636: 7635: 7628: 7605: 7604: 7597: 7587: 7585: 7581: 7570: 7564: 7563: 7556: 7545: 7535: 7533: 7530: 7512:Springer-Verlag 7508:Akademie-Verlag 7499: 7498: 7489: 7447: 7443: 7435: 7431: 7427: 7412: 7410: 7391: 7390: 7375: 7367: 7350: 7349: 7312: 7302: 7300: 7293: 7283: 7252: 7251: 7214: 7190: 7189: 7174: 7131: 7130: 7099: 7092: 7073: 7072: 7068: 7038: 7036: 7020: 7019: 7015: 7006: 7004: 6996: 6995: 6991: 6978:. p. 209. 6972:Springer-Verlag 6954: 6953: 6949: 6940: 6938: 6937:. 9783642980886 6935: 6920: 6919: 6915: 6906: 6904: 6901: 6883:Springer-Verlag 6874: 6873: 6869: 6860: 6858: 6857:. 9783642812415 6855: 6836: 6835: 6831: 6816: 6806:Springer-Verlag 6796: 6795: 6791: 6784: 6763: 6762: 6758: 6751: 6738: 6737: 6733: 6722: 6701: 6700: 6691: 6665: 6663: 6656: 6641: 6622: 6621: 6614: 6605: 6603: 6599: 6588: 6583: 6582: 6578: 6573: 6568: 6567: 6546: 6539: 6522: 6518: 6505: 6501: 6488: 6484: 6479: 6475: 6466: 6462: 6457: 6444: 6422:pseudo-tetrades 6415: 6406: 6401: 6345: 6308: 6254: 6210: 6206: 6178: 6177:, would become 6174: 6173:Meaning number 6088: 6083: 6059: 6045: 6039: 6035: 6021: 6015: 6011: 5997: 5988:Signed leading 5977: 5957: 5923: 5895:Hewlett-Packard 5883: 5874: 5853: 5803: 5798: 5773: 5762: 5761: 5760: 5755: 5744: 5738: 5735: 5692: 5690: 5684: 5680:primary sources 5668: 5653: 5642: 5636: 5633: 5622: 5610: 5569: 5565: 5558: 5553: 5552: 5549: 5546: 5543: 5540: 5537: 5534: 5531: 5528: 5525: 5522: 5519: 5516: 5513: 5510: 5507: 5504: 5501: 5498: 5495: 5492: 5489: 5486: 5483: 5480: 5477: 5474: 5471: 5468: 5465: 5462: 5459: 5456: 5453: 5450: 5447: 5444: 5441: 5438: 5435: 5432: 5429: 5426: 5423: 5420: 5417: 5414: 5411: 5408: 5405: 5402: 5399: 5396: 5393: 5390: 5387: 5384: 5381: 5378: 5375: 5372: 5369: 5366: 5363: 5360: 5357: 5354: 5351: 5348: 5345: 5342: 5339: 5336: 5282: 5280:Other computers 5225:in the digits, 5045:members of the 5039:IBM 1400 series 5015: 5009: 5004: 4991: 4984: 4967:negative number 4963:positive number 4951: 4935:half-carry flag 4927: 4920: 4909: 4904: 4899: 4890: 4280: 4275: 4256: 4235: 4226: 4211: 4148:binary notation 4129: 4112: 4109: 4106: 4105: 4103: 3977: 3972: 3927: 3902: 3899: 3886: 3880: 3874: 3865: 3829:1111 1001 3826:0011 1001 3803:1111 1000 3800:0011 1000 3777:1111 0111 3774:0011 0111 3725:1111 0101 3722:0011 0101 3699:1111 0100 3696:0011 0100 3673:1111 0011 3670:0011 0011 3647:1111 0010 3644:0011 0010 3621:1111 0001 3618:0011 0001 3595:1111 0000 3592:0011 0000 3569:0000 8421 3568: 3562:0000 8421 3561: 3552: 3548: 3544: 3542: 3537: 3531: 3525: 3519: 3513: 3509: 3505: 3503: 3496: 3492: 3488: 3486: 3467: 3463: 3459: 3457: 3452: 3442: 3438: 3434: 3428: 3424: 3420: 3418: 2803: 2738: 2673: 2547: 2420: 2354: 2043: 1978: 1673: 1365: 1302: 1239: 1113: 1047: 981: 463: 462: 224: 216:rounding errors 181:Burroughs B1700 147:pseudo-decimals 138: 35: 28: 23: 22: 15: 12: 11: 5: 9471: 9469: 9461: 9460: 9455: 9450: 9445: 9435: 9434: 9431: 9430: 9425: 9420: 9394: 9366: 9365:External links 9363: 9362: 9361: 9338: 9325: 9319: 9306: 9297: 9284: 9283: 9282: 9249: 9235:(4): 122–126. 9210: 9199: 9178: 9154: 9141: 9112: 9089: 9086: 9083: 9082: 9057: 9048: 9012: 8972: 8932: 8901: 8891:. p. 15. 8877: 8861: 8854: 8844:(3 ed.). 8830: 8795: 8759: 8726: 8643: 8610: 8578: 8575:on 2016-01-14. 8560: 8542: 8525: 8511: 8490: 8471: 8452: 8436: 8430:. p. 14. 8418:(1 ed.). 8403: 8375:(4): 449–458. 8353: 8298: 8257: 8237:(4): 158–159. 8219: 8155: 8091: 8072: 8048: 8011: 7979: 7937: 7904: 7862: 7814: 7773: 7757:Electronic Hub 7744: 7686: 7659: 7626: 7595: 7554: 7543:Éditions Dunod 7528: 7514:. p. 46. 7487: 7445: 7441: 7433: 7429: 7425: 7416:. p. 52: 7373: 7365: 7359:. p. 50. 7310: 7291: 7281: 7212: 7172: 7160:original Kautz 7097: 7090: 7066: 7013: 6989: 6947: 6934:978-3642980886 6933: 6913: 6900:978-3642876639 6899: 6867: 6854:978-3642812415 6853: 6829: 6814: 6789: 6782: 6756: 6749: 6731: 6724:. p. 25: 6720: 6689: 6654: 6612: 6575: 6574: 6572: 6569: 6566: 6565: 6537: 6516: 6499: 6491:Petherick code 6482: 6473: 6460: 6442: 6403: 6402: 6400: 6397: 6396: 6395: 6390: 6384: 6378: 6373: 6368: 6363: 6357: 6351: 6344: 6341: 6307: 6304: 6253: 6250: 6205: 6202: 6200:(SUPI), et.c. 6139: 6138: 6135: 6131: 6130: 6127: 6123: 6122: 6119: 6115: 6114: 6111: 6107: 6106: 6103: 6099: 6098: 6095: 6091: 6090: 6085: 6058: 6055: 6052: 6051: 6043: 6032: 6028: 6027: 6019: 6008: 6004: 6003: 5995: 5992: 5985: 5984: 5975: 5972: 5965: 5964: 5955: 5949: 5943: 5942: 5939: 5936: 5922: 5919: 5899:floating-point 5882: 5879: 5878: 5877: 5872: 5869: 5857: 5852: 5849: 5848: 5847: 5843: 5816: 5813: 5807: 5802: 5799: 5797: 5794: 5775: 5774: 5757: 5756: 5671: 5669: 5662: 5655: 5654: 5613: 5611: 5604: 5599: 5573: 5572: 5570: 5563: 5557: 5554: 5335: 5281: 5278: 5265:z/Architecture 5011:Main article: 5008: 5005: 5003: 5000: 4989: 4982: 4950: 4947: 4925: 4918: 4908: 4905: 4903: 4900: 4897: 4889: 4886: 4873: 4872: 4869: 4866: 4863: 4860: 4857: 4854: 4851: 4848: 4844: 4843: 4840: 4837: 4834: 4831: 4828: 4825: 4822: 4819: 4815: 4814: 4811: 4808: 4805: 4802: 4799: 4796: 4793: 4790: 4786: 4785: 4782: 4779: 4776: 4773: 4770: 4767: 4764: 4761: 4757: 4756: 4753: 4750: 4747: 4744: 4741: 4738: 4735: 4732: 4728: 4727: 4724: 4721: 4718: 4715: 4712: 4709: 4706: 4703: 4699: 4698: 4695: 4692: 4689: 4686: 4683: 4680: 4677: 4674: 4670: 4669: 4666: 4663: 4660: 4657: 4654: 4651: 4648: 4645: 4641: 4640: 4637: 4634: 4631: 4628: 4625: 4622: 4619: 4616: 4612: 4611: 4608: 4605: 4602: 4599: 4596: 4593: 4590: 4587: 4583: 4582: 4579: 4576: 4573: 4570: 4567: 4564: 4561: 4558: 4554: 4553: 4550: 4547: 4544: 4541: 4538: 4535: 4532: 4529: 4525: 4524: 4521: 4518: 4515: 4512: 4509: 4506: 4503: 4500: 4496: 4495: 4492: 4489: 4486: 4483: 4480: 4477: 4474: 4471: 4467: 4466: 4463: 4460: 4457: 4454: 4451: 4448: 4445: 4442: 4438: 4437: 4434: 4431: 4428: 4425: 4422: 4419: 4416: 4413: 4409: 4408: 4405: 4402: 4399: 4396: 4393: 4390: 4387: 4384: 4380: 4379: 4376: 4373: 4370: 4367: 4364: 4361: 4358: 4355: 4351: 4350: 4347: 4344: 4341: 4338: 4335: 4332: 4329: 4326: 4322: 4321: 4318: 4315: 4312: 4309: 4306: 4303: 4300: 4297: 4293: 4292: 4289: 4286: 4279: 4276: 4273: 4255: 4252: 4234: 4231: 4221: 4210: 4207: 4127: 4082: 4081: 4078: 4073: 4070: 4066: 4065: 4062: 4057: 4054: 4050: 4049: 4046: 4041: 4038: 4034: 4033: 4030: 4025: 4022: 4018: 4017: 4014: 4009: 4006: 4002: 4001: 3998: 3993: 3990: 3986: 3985: 3982: 3979: 3974: 3935:packed decimal 3926: 3923: 3897: 3878: 3872: 3862: 3861: 3847: 3831: 3830: 3827: 3824: 3821: 3818: 3815: 3812: 3809: 3805: 3804: 3801: 3798: 3795: 3792: 3789: 3786: 3783: 3779: 3778: 3775: 3772: 3769: 3766: 3763: 3760: 3757: 3753: 3752: 3749: 3746: 3743: 3740: 3737: 3734: 3731: 3727: 3726: 3723: 3720: 3717: 3714: 3711: 3708: 3705: 3701: 3700: 3697: 3694: 3691: 3688: 3685: 3682: 3679: 3675: 3674: 3671: 3668: 3665: 3662: 3659: 3656: 3653: 3649: 3648: 3645: 3642: 3639: 3636: 3633: 3630: 3627: 3623: 3622: 3619: 3616: 3613: 3610: 3607: 3604: 3601: 3597: 3596: 3593: 3590: 3587: 3584: 3581: 3578: 3575: 3571: 3570: 3563: 3556: 3517: 3500: 3480: 3476: code or 3471: 3454: 3409: 3408: 3406: 3403: 3400: 3397: 3394: 3391: 3388: 3385: 3382: 3379: 3376: 3373: 3370: 3367: 3364: 3361: 3358: 3354: 3353: 3350: 3349: 3347: 3344: 3341: 3338: 3335: 3332: 3329: 3326: 3323: 3320: 3317: 3314: 3311: 3308: 3305: 3302: 3299: 3293: 3292: 3289: 3288: 3286: 3283: 3280: 3277: 3274: 3271: 3268: 3265: 3262: 3259: 3256: 3253: 3250: 3247: 3244: 3241: 3238: 3232: 3231: 3228: 3227: 3225: 3222: 3219: 3216: 3213: 3210: 3207: 3204: 3201: 3198: 3195: 3192: 3189: 3186: 3183: 3180: 3177: 3171: 3170: 3167: 3166: 3164: 3161: 3158: 3155: 3152: 3149: 3146: 3143: 3140: 3137: 3134: 3131: 3128: 3125: 3122: 3119: 3116: 3110: 3109: 3106: 3105: 3103: 3100: 3097: 3094: 3091: 3088: 3085: 3082: 3079: 3076: 3073: 3070: 3067: 3064: 3061: 3058: 3055: 3047: 3046: 3043: 3042: 3040: 3037: 3034: 3031: 3028: 3025: 3022: 3019: 3016: 3013: 3010: 3007: 3004: 3001: 2998: 2995: 2992: 2986: 2985: 2982: 2981: 2979: 2976: 2973: 2970: 2967: 2964: 2961: 2958: 2955: 2952: 2949: 2946: 2943: 2940: 2937: 2934: 2931: 2925: 2924: 2921: 2920: 2918: 2915: 2912: 2909: 2906: 2903: 2900: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2876: 2873: 2870: 2864: 2863: 2860: 2859: 2857: 2854: 2851: 2848: 2845: 2842: 2839: 2836: 2833: 2830: 2827: 2824: 2821: 2818: 2815: 2812: 2809: 2799: 2798: 2795: 2794: 2792: 2789: 2786: 2783: 2780: 2777: 2774: 2771: 2768: 2765: 2762: 2759: 2756: 2753: 2750: 2747: 2744: 2734: 2733: 2730: 2729: 2727: 2724: 2721: 2718: 2715: 2712: 2709: 2706: 2703: 2700: 2697: 2694: 2691: 2688: 2685: 2682: 2679: 2669: 2668: 2665: 2664: 2662: 2659: 2656: 2653: 2650: 2647: 2644: 2641: 2638: 2635: 2632: 2629: 2626: 2623: 2620: 2617: 2614: 2608: 2607: 2604: 2603: 2601: 2598: 2595: 2592: 2589: 2586: 2583: 2580: 2577: 2574: 2571: 2568: 2565: 2562: 2559: 2556: 2553: 2543: 2542: 2539: 2538: 2536: 2533: 2530: 2527: 2524: 2521: 2518: 2515: 2512: 2509: 2506: 2503: 2500: 2497: 2494: 2491: 2488: 2482: 2481: 2478: 2477: 2475: 2472: 2469: 2466: 2463: 2460: 2457: 2454: 2451: 2448: 2445: 2442: 2439: 2436: 2433: 2430: 2427: 2416: 2415: 2412: 2411: 2409: 2406: 2403: 2400: 2397: 2394: 2391: 2388: 2385: 2382: 2379: 2376: 2373: 2370: 2367: 2364: 2361: 2350: 2349: 2346: 2345: 2343: 2340: 2337: 2334: 2331: 2328: 2325: 2322: 2319: 2316: 2313: 2310: 2307: 2304: 2301: 2298: 2295: 2289: 2288: 2285: 2284: 2282: 2279: 2276: 2273: 2270: 2267: 2264: 2261: 2258: 2255: 2252: 2249: 2246: 2243: 2240: 2237: 2234: 2226: 2225: 2222: 2221: 2219: 2216: 2213: 2210: 2207: 2204: 2201: 2198: 2195: 2192: 2189: 2186: 2183: 2180: 2177: 2174: 2171: 2165: 2164: 2161: 2160: 2158: 2155: 2152: 2149: 2146: 2143: 2140: 2137: 2134: 2131: 2128: 2125: 2122: 2119: 2116: 2113: 2110: 2104: 2103: 2100: 2099: 2097: 2094: 2091: 2088: 2085: 2082: 2079: 2076: 2073: 2070: 2067: 2064: 2061: 2058: 2055: 2052: 2049: 2039: 2038: 2035: 2034: 2032: 2029: 2026: 2023: 2020: 2017: 2014: 2011: 2008: 2005: 2002: 1999: 1996: 1993: 1990: 1987: 1984: 1974: 1973: 1970: 1969: 1967: 1964: 1961: 1958: 1955: 1952: 1949: 1946: 1943: 1940: 1937: 1934: 1931: 1928: 1925: 1922: 1919: 1913: 1912: 1909: 1908: 1906: 1903: 1900: 1897: 1894: 1891: 1888: 1885: 1882: 1879: 1876: 1873: 1870: 1867: 1864: 1861: 1858: 1852: 1851: 1848: 1847: 1845: 1842: 1839: 1836: 1833: 1830: 1827: 1824: 1821: 1818: 1815: 1812: 1809: 1806: 1803: 1800: 1797: 1793: 1792: 1789: 1788: 1786: 1783: 1780: 1777: 1774: 1771: 1768: 1765: 1762: 1759: 1756: 1753: 1750: 1747: 1744: 1741: 1738: 1732: 1731: 1728: 1727: 1725: 1722: 1719: 1716: 1713: 1710: 1707: 1704: 1701: 1698: 1695: 1692: 1689: 1686: 1683: 1680: 1677: 1669: 1668: 1665: 1664: 1662: 1659: 1656: 1653: 1650: 1647: 1644: 1641: 1638: 1635: 1632: 1629: 1626: 1623: 1620: 1617: 1614: 1608: 1607: 1604: 1603: 1601: 1598: 1595: 1592: 1589: 1586: 1583: 1580: 1577: 1574: 1571: 1568: 1565: 1562: 1559: 1556: 1553: 1547: 1546: 1543: 1542: 1540: 1537: 1534: 1531: 1528: 1525: 1522: 1519: 1516: 1513: 1510: 1507: 1504: 1501: 1498: 1495: 1492: 1486: 1485: 1482: 1481: 1479: 1476: 1473: 1470: 1467: 1464: 1461: 1458: 1455: 1452: 1449: 1446: 1443: 1440: 1437: 1434: 1431: 1425: 1424: 1421: 1420: 1418: 1415: 1412: 1409: 1406: 1403: 1400: 1397: 1394: 1391: 1388: 1385: 1382: 1379: 1376: 1373: 1370: 1362: 1361: 1358: 1357: 1355: 1352: 1349: 1346: 1343: 1340: 1337: 1334: 1331: 1328: 1325: 1322: 1319: 1316: 1313: 1310: 1307: 1299: 1298: 1295: 1294: 1292: 1289: 1286: 1283: 1280: 1277: 1274: 1271: 1268: 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1244: 1236: 1235: 1232: 1231: 1229: 1226: 1223: 1220: 1217: 1214: 1211: 1208: 1205: 1202: 1199: 1196: 1193: 1190: 1187: 1184: 1181: 1175: 1174: 1171: 1170: 1168: 1165: 1162: 1159: 1156: 1153: 1150: 1147: 1144: 1141: 1138: 1135: 1132: 1129: 1126: 1123: 1120: 1109: 1108: 1105: 1104: 1102: 1099: 1096: 1093: 1090: 1087: 1084: 1081: 1078: 1075: 1072: 1069: 1066: 1063: 1060: 1057: 1054: 1043: 1042: 1039: 1038: 1036: 1033: 1030: 1027: 1024: 1021: 1018: 1015: 1012: 1009: 1006: 1003: 1000: 997: 994: 991: 988: 977: 976: 973: 972: 970: 967: 964: 961: 958: 955: 952: 949: 946: 943: 940: 937: 934: 931: 928: 925: 922: 916: 915: 912: 911: 909: 906: 903: 900: 897: 894: 891: 888: 885: 882: 879: 876: 873: 870: 867: 864: 861: 855: 854: 851: 850: 845: 842: 839: 836: 833: 830: 827: 824: 821: 818: 815: 812: 809: 806: 803: 800: 797: 791: 790: 787: 786: 783: 780: 777: 774: 771: 768: 765: 762: 759: 756: 753: 750: 747: 744: 741: 738: 735: 731: 730: 727: 724: 721: 718: 715: 712: 709: 706: 703: 700: 697: 694: 691: 688: 685: 682: 679: 675: 674: 671: 668: 665: 662: 659: 656: 653: 650: 647: 644: 641: 638: 635: 632: 629: 626: 623: 619: 618: 613: 610: 607: 604: 601: 598: 595: 592: 589: 586: 583: 580: 577: 574: 571: 568: 565: 562: 558: 557: 554: 551: 548: 545: 542: 539: 536: 533: 530: 527: 524: 521: 518: 515: 512: 509: 506: 503: 482: 479: 476: 473: 470: 425: 424: 421: 418: 415: 412: 408: 407: 404: 401: 398: 395: 391: 390: 387: 384: 381: 378: 374: 373: 370: 367: 364: 361: 357: 356: 353: 350: 347: 344: 340: 339: 336: 333: 330: 327: 323: 322: 319: 316: 313: 310: 306: 305: 302: 299: 296: 293: 289: 288: 285: 282: 279: 276: 272: 271: 268: 265: 262: 259: 255: 254: 251: 248: 245: 241: 240: 237: 236:Decimal digit 223: 220: 212:floating-point 169:IBM System/360 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 9470: 9459: 9456: 9454: 9451: 9449: 9446: 9444: 9441: 9440: 9438: 9429: 9426: 9424: 9421: 9411: 9407: 9403: 9399: 9395: 9385: 9381: 9377: 9373: 9369: 9368: 9364: 9351: 9347: 9343: 9339: 9335: 9331: 9326: 9322: 9320:1-60132-009-4 9316: 9312: 9307: 9303: 9298: 9294: 9290: 9285: 9279: 9275: 9271: 9270: 9256: 9252: 9250:0-8186-0805-6 9246: 9242: 9238: 9234: 9230: 9223: 9219: 9215: 9211: 9208: 9202: 9200:0-89874-318-4 9196: 9192: 9188: 9181: 9179:0-471-76180-X 9175: 9171: 9166: 9165: 9159: 9155: 9151: 9147: 9142: 9127: 9123: 9119: 9115: 9109: 9106: 9099: 9098: 9092: 9091: 9087: 9079: 9076: 9072: 9068: 9067: 9061: 9058: 9052: 9049: 9037:on 2008-10-10 9033: 9029: 9022: 9016: 9013: 8997: 8993: 8989: 8982: 8976: 8973: 8957: 8953: 8949: 8942: 8936: 8933: 8922:on 2015-02-21 8918: 8911: 8905: 8902: 8894: 8887: 8881: 8878: 8873: 8872: 8865: 8862: 8857: 8851: 8847: 8843: 8842: 8834: 8831: 8816: 8812: 8805: 8799: 8796: 8781: 8777: 8770: 8763: 8760: 8748: 8744: 8740: 8736: 8730: 8727: 8724: 8721: 8719: 8714: 8710: 8706: 8702: 8698: 8694: 8691: 8687: 8683: 8667: 8663: 8656: 8655: 8647: 8644: 8629: 8622: 8621: 8614: 8611: 8595: 8588: 8582: 8579: 8574: 8570: 8564: 8561: 8556: 8552: 8546: 8543: 8535: 8529: 8526: 8521: 8515: 8512: 8507: 8503: 8497: 8495: 8491: 8486: 8482: 8475: 8472: 8468:. March 1980. 8467: 8463: 8456: 8453: 8447: 8443: 8439: 8437:0-07-016638-2 8433: 8429: 8425: 8421: 8417: 8413: 8407: 8404: 8398: 8394: 8390: 8386: 8382: 8378: 8374: 8370: 8369: 8364: 8357: 8354: 8342: 8338: 8334: 8330: 8326: 8322: 8318: 8317: 8312: 8305: 8303: 8299: 8295: 8291: 8285: 8281: 8277: 8273: 8266: 8264: 8262: 8258: 8252: 8248: 8244: 8240: 8236: 8232: 8231: 8223: 8220: 8208:on 2020-05-18 8207: 8203: 8199: 8195: 8191: 8187: 8183: 8179: 8175: 8174: 8169: 8162: 8160: 8156: 8144:on 2020-05-18 8143: 8139: 8135: 8131: 8127: 8123: 8119: 8115: 8111: 8110: 8105: 8098: 8096: 8092: 8087: 8083: 8076: 8073: 8069: 8063: 8059: 8052: 8049: 8037: 8033: 8029: 8022: 8020: 8018: 8016: 8012: 8008: 8004: 8001: 7986: 7982: 7976: 7972: 7968: 7964: 7960: 7956: 7952: 7948: 7944: 7940: 7934: 7930: 7923: 7922: 7917: 7911: 7909: 7905: 7899: 7895: 7891: 7887: 7883: 7879: 7878: 7873: 7866: 7863: 7847: 7842: 7837: 7830: 7829: 7824: 7818: 7815: 7811: 7807: 7803: 7802:Gray BCD code 7798: 7797:Schleifencode 7784: 7777: 7774: 7762: 7758: 7754: 7748: 7745: 7739: 7735: 7731: 7727: 7723: 7719: 7715: 7711: 7707: 7703: 7699: 7698: 7690: 7687: 7684: 7678: 7674: 7670: 7666: 7662: 7660:3-540-05058-2 7656: 7652: 7648: 7644: 7640: 7633: 7631: 7627: 7621: 7617: 7614:(in German). 7613: 7609: 7602: 7600: 7596: 7580: 7576: 7569: 7568: 7561: 7559: 7555: 7549: 7544: 7531: 7525: 7521: 7517: 7513: 7509: 7505: 7504: 7496: 7494: 7492: 7488: 7484: 7480: 7476: 7472: 7470: 7468: 7466: 7464: 7462: 7460: 7458: 7456: 7454: 7452: 7449: 7439: 7422: 7408: 7404: 7400: 7399: 7394: 7388: 7386: 7384: 7382: 7380: 7378: 7374: 7368: 7366:3-87145-272-6 7362: 7358: 7354: 7347: 7345: 7343: 7341: 7339: 7337: 7335: 7333: 7331: 7329: 7327: 7325: 7323: 7321: 7319: 7317: 7315: 7311: 7299:on 2020-07-16 7298: 7294: 7288: 7284: 7278: 7274: 7270: 7266: 7262: 7258: 7257: 7249: 7247: 7245: 7243: 7241: 7239: 7237: 7235: 7233: 7231: 7229: 7227: 7225: 7223: 7221: 7219: 7217: 7213: 7207: 7203: 7202: 7197: 7196:Frühauf, Hans 7193: 7187: 7185: 7183: 7181: 7179: 7177: 7173: 7169: 7168:9s complement 7165: 7161: 7157: 7151: 7147: 7143: 7139: 7135: 7128: 7126: 7124: 7122: 7120: 7118: 7116: 7114: 7112: 7110: 7108: 7106: 7104: 7102: 7098: 7093: 7087: 7083: 7079: 7078: 7070: 7067: 7063: 7062:Ferranti code 7059: 7055: 7051: 7047: 7034: 7030: 7026: 7025: 7017: 7014: 7003: 6999: 6993: 6990: 6985: 6981: 6977: 6973: 6969: 6965: 6961: 6957: 6951: 6948: 6936: 6930: 6926: 6925: 6917: 6914: 6902: 6896: 6892: 6888: 6884: 6880: 6879: 6871: 6868: 6856: 6850: 6846: 6842: 6841: 6833: 6830: 6825: 6821: 6817: 6815:3-540-06241-6 6811: 6807: 6803: 6799: 6793: 6790: 6785: 6783:3-446-10569-7 6779: 6775: 6771: 6767: 6760: 6757: 6752: 6750:3-486-22662-2 6746: 6742: 6735: 6732: 6727: 6723: 6717: 6713: 6709: 6705: 6698: 6696: 6694: 6690: 6686: 6682: 6678: 6674: 6661: 6657: 6655:3-11-083160-0 6651: 6645: 6640: 6636: 6632: 6628: 6627: 6619: 6617: 6613: 6598: 6594: 6587: 6580: 6577: 6570: 6562: 6558: 6554: 6553:minicomputers 6550: 6544: 6542: 6538: 6534: 6530: 6526: 6520: 6517: 6513: 6509: 6503: 6500: 6496: 6492: 6486: 6483: 6477: 6474: 6470: 6464: 6461: 6455: 6453: 6451: 6449: 6447: 6443: 6439: 6438:unused states 6435: 6431: 6427: 6423: 6419: 6413: 6411: 6409: 6405: 6398: 6394: 6391: 6388: 6387:Double dabble 6385: 6382: 6379: 6377: 6374: 6372: 6369: 6367: 6364: 6361: 6358: 6355: 6352: 6350: 6347: 6346: 6342: 6340: 6338: 6334: 6329: 6327: 6323: 6320:overturned a 6319: 6315: 6314: 6306:Legal history 6305: 6303: 6301: 6297: 6293: 6292:PlayStation 3 6288: 6286: 6282: 6278: 6273: 6271: 6267: 6263: 6259: 6251: 6249: 6247: 6246:IEEE 754-2008 6243: 6239: 6235: 6231: 6226: 6224: 6220: 6214: 6203: 6201: 6199: 6195: 6191: 6187: 6182: 6170: 6168: 6164: 6159: 6158: 6154: 6148: 6146: 6136: 6133: 6132: 6128: 6125: 6124: 6120: 6117: 6116: 6112: 6109: 6108: 6104: 6101: 6100: 6096: 6093: 6092: 6086: 6081: 6080: 6077: 6075: 6071: 6067: 6063: 6056: 6048: 6044: 6033: 6030: 6029: 6025: 6020: 6009: 6006: 6005: 6000: 5996: 5993: 5991: 5987: 5986: 5981: 5976: 5973: 5971: 5967: 5966: 5961: 5956: 5954: 5950: 5948: 5945: 5944: 5940: 5937: 5934: 5933: 5930: 5928: 5920: 5918: 5916: 5912: 5908: 5904: 5900: 5896: 5892: 5888: 5880: 5870: 5867: 5862: 5858: 5855: 5854: 5851:Disadvantages 5850: 5844: 5841: 5837: 5833: 5829: 5825: 5821: 5817: 5814: 5811: 5808: 5805: 5804: 5800: 5795: 5793: 5789: 5786: 5781: 5771: 5768: 5753: 5750: 5742: 5731: 5728: 5724: 5721: 5717: 5714: 5710: 5707: 5703: 5700: – 5699: 5695: 5694:Find sources: 5688: 5682: 5681: 5677: 5672:This section 5670: 5666: 5661: 5660: 5651: 5648: 5640: 5630: 5626: 5620: 5619: 5614:This section 5612: 5608: 5603: 5602: 5597: 5595: 5588: 5587: 5582: 5581: 5576: 5571: 5562: 5561: 5555: 5529:// correction 5333: 5331: 5325: 5321: 5319: 5315: 5311: 5307: 5303: 5298: 5296: 5291: 5287: 5279: 5277: 5274: 5270: 5266: 5262: 5257: 5255: 5251: 5246: 5244: 5240: 5236: 5231: 5228: 5224: 5220: 5217: 5213: 5209: 5204: 5202: 5198: 5194: 5190: 5186: 5182: 5178: 5173: 5171: 5167: 5163: 5159: 5155: 5151: 5147: 5143: 5139: 5135: 5131: 5127: 5123: 5119: 5115: 5111: 5107: 5103: 5099: 5095: 5091: 5087: 5083: 5079: 5075: 5071: 5067: 5063: 5059: 5055: 5054:B, A, 8, 4, 2 5050: 5048: 5044: 5040: 5036: 5032: 5028: 5027: 5022: 5021: 5014: 5006: 5001: 4999: 4995: 4988: 4981: 4978: 4975: 4970: 4968: 4964: 4960: 4956: 4948: 4946: 4944: 4940: 4936: 4930: 4924: 4917: 4914: 4906: 4901: 4896: 4893: 4887: 4885: 4884: 4882: 4870: 4867: 4864: 4861: 4858: 4855: 4852: 4849: 4846: 4845: 4841: 4838: 4835: 4832: 4829: 4826: 4823: 4820: 4817: 4816: 4812: 4809: 4806: 4803: 4800: 4797: 4794: 4791: 4788: 4787: 4783: 4780: 4777: 4774: 4771: 4768: 4765: 4762: 4759: 4758: 4754: 4751: 4748: 4745: 4742: 4739: 4736: 4733: 4730: 4729: 4725: 4722: 4719: 4716: 4713: 4710: 4707: 4704: 4701: 4700: 4696: 4693: 4690: 4687: 4684: 4681: 4678: 4675: 4672: 4671: 4667: 4664: 4661: 4658: 4655: 4652: 4649: 4646: 4643: 4642: 4638: 4635: 4632: 4629: 4626: 4623: 4620: 4617: 4614: 4613: 4609: 4606: 4603: 4600: 4597: 4594: 4591: 4588: 4585: 4584: 4580: 4577: 4574: 4571: 4568: 4565: 4562: 4559: 4556: 4555: 4551: 4548: 4545: 4542: 4539: 4536: 4533: 4530: 4527: 4526: 4522: 4519: 4516: 4513: 4510: 4507: 4504: 4501: 4498: 4497: 4493: 4490: 4487: 4484: 4481: 4478: 4475: 4472: 4469: 4468: 4464: 4461: 4458: 4455: 4452: 4449: 4446: 4443: 4440: 4439: 4435: 4432: 4429: 4426: 4423: 4420: 4417: 4414: 4411: 4410: 4406: 4403: 4400: 4397: 4394: 4391: 4388: 4385: 4382: 4381: 4377: 4374: 4371: 4368: 4365: 4362: 4359: 4356: 4353: 4352: 4348: 4345: 4342: 4339: 4336: 4333: 4330: 4327: 4324: 4323: 4319: 4316: 4313: 4310: 4307: 4304: 4301: 4298: 4295: 4294: 4284: 4283: 4277: 4272: 4268: 4265: 4264:zoned decimal 4261: 4254:Zoned decimal 4253: 4251: 4249: 4248: 4243: 4242: 4232: 4230: 4225: 4220: 4217: 4215: 4208: 4206: 4202: 4199: 4195: 4193: 4189: 4185: 4181: 4177: 4173: 4169: 4164: 4162: 4157: 4153: 4149: 4144: 4142: 4137: 4135: 4126: 4123: 4121: 4101: 4097: 4093: 4089: 4079: 4077: 4074: 4071: 4068: 4067: 4063: 4061: 4058: 4055: 4052: 4051: 4047: 4045: 4042: 4039: 4036: 4035: 4031: 4029: 4026: 4023: 4020: 4019: 4015: 4013: 4010: 4007: 4004: 4003: 3999: 3997: 3994: 3991: 3988: 3987: 3983: 3980: 3975: 3970: 3969: 3966: 3962: 3960: 3956: 3952: 3946: 3944: 3940: 3936: 3932: 3924: 3922: 3920: 3916: 3912: 3908: 3905: 3896: 3894: 3889: 3883: 3877: 3871: 3868: 3859: 3855: 3851: 3848: 3845: 3842: 3841: 3840: 3838: 3828: 3825: 3822: 3819: 3816: 3813: 3810: 3807: 3806: 3802: 3799: 3796: 3793: 3790: 3787: 3784: 3781: 3780: 3776: 3773: 3770: 3767: 3764: 3761: 3758: 3755: 3754: 3750: 3747: 3744: 3741: 3738: 3735: 3732: 3729: 3728: 3724: 3721: 3718: 3715: 3712: 3709: 3706: 3703: 3702: 3698: 3695: 3692: 3689: 3686: 3683: 3680: 3677: 3676: 3672: 3669: 3666: 3663: 3660: 3657: 3654: 3651: 3650: 3646: 3643: 3640: 3637: 3634: 3631: 3628: 3625: 3624: 3620: 3617: 3614: 3611: 3608: 3605: 3602: 3599: 3598: 3594: 3591: 3588: 3585: 3582: 3579: 3576: 3573: 3572: 3567: 3564: 3560: 3557: 3540: 3534: 3528: 3522: 3518: 3501: 3484: 3481: 3479: 3475: 3472: 3455: 3450: 3449: 3446: 3416: 3407: 3404: 3401: 3398: 3395: 3392: 3389: 3386: 3383: 3380: 3377: 3374: 3371: 3368: 3365: 3362: 3359: 3355: 3351: 3348: 3345: 3342: 3339: 3336: 3333: 3330: 3327: 3324: 3321: 3318: 3315: 3312: 3309: 3306: 3303: 3300: 3298: 3294: 3290: 3287: 3284: 3281: 3278: 3275: 3272: 3269: 3266: 3263: 3260: 3257: 3254: 3251: 3248: 3245: 3242: 3239: 3237: 3233: 3229: 3226: 3223: 3220: 3217: 3214: 3211: 3208: 3205: 3202: 3199: 3196: 3193: 3190: 3187: 3184: 3181: 3178: 3176: 3172: 3168: 3165: 3162: 3159: 3156: 3153: 3150: 3147: 3144: 3141: 3138: 3135: 3132: 3129: 3126: 3123: 3120: 3117: 3115: 3111: 3107: 3104: 3101: 3098: 3095: 3092: 3089: 3086: 3083: 3080: 3077: 3074: 3071: 3068: 3065: 3062: 3059: 3056: 3054: 3053: 3048: 3044: 3041: 3038: 3035: 3032: 3029: 3026: 3023: 3020: 3017: 3014: 3011: 3008: 3005: 3002: 2999: 2996: 2993: 2991: 2987: 2983: 2980: 2977: 2974: 2971: 2968: 2965: 2962: 2959: 2956: 2953: 2950: 2947: 2944: 2941: 2938: 2935: 2932: 2930: 2926: 2922: 2919: 2916: 2913: 2910: 2907: 2904: 2901: 2898: 2895: 2892: 2889: 2886: 2883: 2880: 2877: 2874: 2871: 2869: 2865: 2861: 2858: 2855: 2852: 2849: 2846: 2843: 2840: 2837: 2834: 2831: 2828: 2825: 2822: 2819: 2816: 2813: 2810: 2808: 2806: 2805:Excess-3 Gray 2800: 2796: 2793: 2790: 2787: 2784: 2781: 2778: 2775: 2772: 2769: 2766: 2763: 2760: 2757: 2754: 2751: 2748: 2745: 2743: 2741: 2735: 2731: 2728: 2725: 2722: 2719: 2716: 2713: 2710: 2707: 2704: 2701: 2698: 2695: 2692: 2689: 2686: 2683: 2680: 2678: 2676: 2670: 2666: 2663: 2660: 2657: 2654: 2651: 2648: 2645: 2642: 2639: 2636: 2633: 2630: 2627: 2624: 2621: 2618: 2615: 2613: 2609: 2605: 2602: 2599: 2596: 2593: 2590: 2587: 2584: 2581: 2578: 2575: 2572: 2569: 2566: 2563: 2560: 2557: 2554: 2552: 2550: 2544: 2540: 2537: 2534: 2531: 2528: 2525: 2522: 2519: 2516: 2513: 2510: 2507: 2504: 2501: 2498: 2495: 2492: 2489: 2487: 2483: 2479: 2476: 2473: 2470: 2467: 2464: 2461: 2458: 2455: 2452: 2449: 2446: 2443: 2440: 2437: 2434: 2431: 2428: 2426: 2423: 2417: 2413: 2410: 2407: 2404: 2401: 2398: 2395: 2392: 2389: 2386: 2383: 2380: 2377: 2374: 2371: 2368: 2365: 2362: 2360: 2357: 2351: 2347: 2344: 2341: 2338: 2335: 2332: 2329: 2326: 2323: 2320: 2317: 2314: 2311: 2308: 2305: 2302: 2299: 2296: 2294: 2290: 2286: 2283: 2280: 2277: 2274: 2271: 2268: 2265: 2262: 2259: 2256: 2253: 2250: 2247: 2244: 2241: 2238: 2235: 2233: 2232: 2227: 2223: 2220: 2217: 2214: 2211: 2208: 2205: 2202: 2199: 2196: 2193: 2190: 2187: 2184: 2181: 2178: 2175: 2172: 2170: 2166: 2162: 2159: 2156: 2153: 2150: 2147: 2144: 2141: 2138: 2135: 2132: 2129: 2126: 2123: 2120: 2117: 2114: 2111: 2109: 2105: 2101: 2098: 2095: 2092: 2089: 2086: 2083: 2080: 2077: 2074: 2071: 2068: 2065: 2062: 2059: 2056: 2053: 2050: 2048: 2046: 2040: 2036: 2033: 2030: 2027: 2024: 2021: 2018: 2015: 2012: 2009: 2006: 2003: 2000: 1997: 1994: 1991: 1988: 1985: 1983: 1981: 1975: 1971: 1968: 1965: 1962: 1959: 1956: 1953: 1950: 1947: 1944: 1941: 1938: 1935: 1932: 1929: 1926: 1923: 1920: 1918: 1914: 1910: 1907: 1904: 1901: 1898: 1895: 1892: 1889: 1886: 1883: 1880: 1877: 1874: 1871: 1868: 1865: 1862: 1859: 1857: 1853: 1849: 1846: 1843: 1840: 1837: 1834: 1831: 1828: 1825: 1822: 1819: 1816: 1813: 1810: 1807: 1804: 1801: 1798: 1794: 1790: 1787: 1784: 1781: 1778: 1775: 1772: 1769: 1766: 1763: 1760: 1757: 1754: 1751: 1748: 1745: 1742: 1739: 1737: 1733: 1729: 1726: 1723: 1720: 1717: 1714: 1711: 1708: 1705: 1702: 1699: 1696: 1693: 1690: 1687: 1684: 1681: 1678: 1676: 1670: 1666: 1663: 1660: 1657: 1654: 1651: 1648: 1645: 1642: 1639: 1636: 1633: 1630: 1627: 1624: 1621: 1618: 1615: 1613: 1609: 1605: 1602: 1599: 1596: 1593: 1590: 1587: 1584: 1581: 1578: 1575: 1572: 1569: 1566: 1563: 1560: 1557: 1554: 1552: 1548: 1544: 1541: 1538: 1535: 1532: 1529: 1526: 1523: 1520: 1517: 1514: 1511: 1508: 1505: 1502: 1499: 1496: 1493: 1491: 1487: 1483: 1480: 1477: 1474: 1471: 1468: 1465: 1462: 1459: 1456: 1453: 1450: 1447: 1444: 1441: 1438: 1435: 1432: 1430: 1426: 1422: 1419: 1416: 1413: 1410: 1407: 1404: 1401: 1398: 1395: 1392: 1389: 1386: 1383: 1380: 1377: 1374: 1371: 1368: 1363: 1359: 1356: 1353: 1350: 1347: 1344: 1341: 1338: 1335: 1332: 1329: 1326: 1323: 1320: 1317: 1314: 1311: 1308: 1305: 1300: 1296: 1293: 1290: 1287: 1284: 1281: 1278: 1275: 1272: 1269: 1266: 1263: 1260: 1257: 1254: 1251: 1248: 1245: 1242: 1237: 1233: 1230: 1227: 1224: 1221: 1218: 1215: 1212: 1209: 1206: 1203: 1200: 1197: 1194: 1191: 1188: 1185: 1182: 1180: 1176: 1172: 1169: 1166: 1163: 1160: 1157: 1154: 1151: 1148: 1145: 1142: 1139: 1136: 1133: 1130: 1127: 1124: 1121: 1119: 1116: 1110: 1106: 1103: 1100: 1097: 1094: 1091: 1088: 1085: 1082: 1079: 1076: 1073: 1070: 1067: 1064: 1061: 1058: 1055: 1053: 1050: 1044: 1040: 1037: 1034: 1031: 1028: 1025: 1022: 1019: 1016: 1013: 1010: 1007: 1004: 1001: 998: 995: 992: 989: 987: 984: 978: 974: 971: 968: 965: 962: 959: 956: 953: 950: 947: 944: 941: 938: 935: 932: 929: 926: 923: 921: 917: 913: 910: 907: 904: 901: 898: 895: 892: 889: 886: 883: 880: 877: 874: 871: 868: 865: 862: 860: 856: 852: 849: 846: 843: 840: 837: 834: 831: 828: 825: 822: 819: 816: 813: 810: 807: 804: 801: 798: 796: 792: 788: 784: 781: 778: 775: 772: 769: 766: 763: 760: 757: 754: 751: 748: 745: 742: 739: 736: 733: 732: 728: 725: 722: 719: 716: 713: 710: 707: 704: 701: 698: 695: 692: 689: 686: 683: 680: 677: 676: 672: 669: 666: 663: 660: 657: 654: 651: 648: 645: 642: 639: 636: 633: 630: 627: 624: 621: 620: 617: 611: 608: 605: 602: 599: 596: 593: 590: 587: 584: 581: 578: 575: 572: 569: 566: 563: 560: 559: 555: 552: 549: 546: 543: 540: 537: 534: 531: 528: 525: 522: 519: 516: 513: 510: 507: 504: 501: 500: 494: 480: 477: 474: 471: 468: 444: 440: 439:BCD 8421 436: 432: 422: 419: 416: 413: 410: 409: 405: 402: 399: 396: 393: 392: 388: 385: 382: 379: 376: 375: 371: 368: 365: 362: 359: 358: 354: 351: 348: 345: 342: 341: 337: 334: 331: 328: 325: 324: 320: 317: 314: 311: 308: 307: 303: 300: 297: 294: 291: 290: 286: 283: 280: 277: 274: 273: 269: 266: 263: 260: 257: 256: 252: 249: 246: 243: 242: 234: 231: 229: 221: 219: 217: 213: 209: 205: 201: 197: 193: 188: 186: 182: 178: 174: 170: 166: 161: 159: 154: 152: 148: 142: 137: 136: 131: 127: 123: 122: 116: 114: 109: 105: 101: 96: 94: 90: 86: 82: 79:encodings of 78: 74: 70: 66: 62: 54: 50: 46: 41: 37: 33: 19: 9428:BCD for Java 9413:. Retrieved 9405: 9387:. Retrieved 9379: 9354:. Retrieved 9349: 9329: 9310: 9301: 9288: 9277: 9262:. Retrieved 9232: 9228: 9190: 9163: 9150:van Nostrand 9145: 9133:. Retrieved 9096: 9080: (1972). 9064: 9060: 9051: 9039:. Retrieved 9032:the original 9027: 9015: 9003:. Retrieved 8975: 8963:. Retrieved 8935: 8924:. Retrieved 8917:the original 8904: 8880: 8870: 8864: 8840: 8833: 8822:. Retrieved 8798: 8787:. Retrieved 8762: 8751:. Retrieved 8742: 8729: 8679: 8673:. Retrieved 8653: 8646: 8635:. Retrieved 8619: 8613: 8601:. Retrieved 8581: 8573:the original 8563: 8545: 8528: 8514: 8501: 8480: 8474: 8461: 8455: 8415: 8406: 8372: 8366: 8356: 8345:. Retrieved 8320: 8314: 8271: 8234: 8228: 8222: 8210:. Retrieved 8206:the original 8177: 8171: 8146:. Retrieved 8142:the original 8113: 8107: 8081: 8075: 8067: 8057: 8051: 8040:. Retrieved 8031: 8006: 7998: 7992:. Retrieved 7938:0-07036981-X 7920: 7881: 7875: 7865: 7853:. Retrieved 7827: 7817: 7787:. Retrieved 7776: 7765:. Retrieved 7756: 7747: 7701: 7695: 7689: 7638: 7615: 7611: 7586:. Retrieved 7566: 7534:. Retrieved 7502: 7417: 7411:. Retrieved 7397: 7352: 7301:. Retrieved 7297:the original 7255: 7200: 7137: 7076: 7069: 7061: 7037:. Retrieved 7023: 7016: 7005:. Retrieved 6992: 6963: 6959: 6950: 6939:. Retrieved 6923: 6916: 6905:. Retrieved 6877: 6870: 6859:. Retrieved 6839: 6832: 6801: 6792: 6769: 6765: 6759: 6740: 6734: 6725: 6721:3-11011700-2 6707: 6703: 6677:3-11002793-3 6664:. Retrieved 6630: 6625: 6604:. Retrieved 6579: 6561:DEC RADIX 50 6519: 6502: 6485: 6476: 6463: 6330: 6311: 6309: 6289: 6274: 6255: 6227: 6225:is implied. 6215: 6207: 6183: 6172: 6166: 6162: 6160: 6156: 6152: 6150: 6144: 6142: 6065: 6060: 6046: 6023: 5998: 5989: 5979: 5969: 5959: 5938:Description 5924: 5884: 5831: 5790: 5782: 5778: 5763: 5745: 5739:January 2018 5736: 5726: 5719: 5712: 5705: 5693: 5673: 5643: 5637:January 2018 5634: 5623:Please help 5618:verification 5615: 5591: 5584: 5578: 5577:Please help 5574: 5326: 5322: 5312:series. The 5299: 5290:instructions 5283: 5258: 5247: 5242: 5238: 5232: 5226: 5218: 5205: 5200: 5196: 5192: 5188: 5184: 5180: 5176: 5174: 5169: 5165: 5161: 5157: 5153: 5149: 5145: 5141: 5137: 5133: 5129: 5125: 5121: 5117: 5113: 5109: 5105: 5102:punched card 5097: 5093: 5089: 5085: 5081: 5077: 5073: 5069: 5065: 5061: 5057: 5053: 5051: 5030: 5026:alphanumeric 5024: 5018: 5016: 4996: 4992: 4985: 4979: 4971: 4952: 4931: 4928: 4921: 4910: 4894: 4891: 4878: 4876: 4604:^ (*) 4601:} (*) 4288:Hexadecimal 4269: 4263: 4257: 4245: 4239: 4236: 4227: 4223: 4222:12 34 56 7C 4218: 4212: 4203: 4196: 4165: 4145: 4138: 4130: 4124: 4119: 4099: 4095: 4091: 4085: 4075: 4059: 4043: 4027: 4011: 3995: 3963: 3947: 3934: 3930: 3928: 3909: 3903: 3900: 3887: 3884: 3881: 3875: 3866: 3863: 3849: 3843: 3834: 3412: 3296: 3235: 3174: 3113: 3050: 2989: 2928: 2867: 2802: 2737: 2672: 2611: 2546: 2485: 2419: 2353: 2292: 2229: 2168: 2107: 2042: 1977: 1916: 1855: 1735: 1672: 1611: 1550: 1489: 1428: 1366: 1303: 1240: 1178: 1112: 1046: 980: 919: 858: 847: 794: 615: 438: 434: 430: 428: 227: 225: 210:and decimal 191: 189: 162: 155: 150: 146: 134: 119: 117: 107: 103: 97: 72: 68: 58: 45:binary clock 36: 9218:Katz, Randy 9010:(TS 23.003) 8970:(TS 24.501) 7823:Gray, Frank 7683:1st edition 7546: [ 7444:=2 Δ 7292:333-13360-9 7056:to achieve 7052:applied as 6729:(320 pages) 6685:4th edition 6642: [ 6497:(RAE) code. 6322:lower court 6252:Application 6242:significand 6223:radix point 6190:operator ID 6145:TBCD-STRING 5990:(overpunch) 5239:alphamerics 5219:alphamerics 5189:alphamerics 5140:, which is 5031:alphamerics 4987:following: 4949:Subtraction 4224:12 34.56 7+ 4214:Fixed-point 3297:Susskind II 2740:Tompkins II 228:Natural BCD 208:fixed-point 139: [ 53:sexagesimal 9437:Categories 9415:2016-01-02 9389:2016-01-02 9356:2016-01-02 9264:2012-04-25 9135:August 25, 9041:2022-05-22 9005:2022-02-26 8965:2022-02-26 8926:2013-06-27 8824:2015-08-14 8789:2015-08-15 8753:2016-01-03 8709:don't care 8675:2020-08-06 8637:2013-04-23 8608:(58 pages) 8603:2023-11-21 8401:(10 pages) 8347:2020-08-08 8212:2020-05-18 8148:2020-05-18 8042:2018-07-16 7994:2021-02-19 7980:07036981-X 7963:1033638267 7860:(13 pages) 7855:2020-08-05 7789:2008-02-11 7767:2020-08-04 7620:Telefunken 7588:2020-07-25 7536:2020-06-21 7413:2020-07-03 7303:2020-05-11 7058:odd parity 7050:parity bit 7039:2020-05-24 7007:2016-01-02 6968:ETH Zürich 6941:2015-08-05 6907:2015-08-05 6861:2015-08-05 6666:2020-04-13 6606:2015-07-01 6571:References 6557:IBM SQUOZE 6469:Aiken code 6064:developed 5801:Advantages 5709:newspapers 5676:references 5580:improve it 5481:0x11111110 5397:0x06666666 5308:, and the 5276:software. 5271:and later 5235:System/360 5177:8, 4, 2, 1 5041:, and non- 4955:subtrahend 4939:Intel 8080 4285:BCD digit 4134:endianness 4048:Preferred 4032:Preferred 3943:big endian 3931:packed BCD 3925:Packed BCD 3893:big-endian 3751:1111 0110 3748:0011 0110 3483:Aiken-Code 3236:Susskind I 2675:O'Brien II 2549:Tompkins I 459:1001'b 455:0110'b 451:1100'b 447:0110'b 222:Background 130:don't care 65:electronic 47:might use 9400:(2007) . 9374:(2014) . 9344:(2009) . 9207:misprints 9189:(1983) . 9046:(7 pages) 8397:206673385 8389:0367-9950 8255:(2 pages) 8251:0367-9950 8202:0367-9950 8130:0097-2452 8032:quadibloc 7947:2574-7916 7902:(5 pages) 7898:0010-8049 7892:: 87–91. 7810:slip ring 7742:(3 pages) 7730:0096-8390 7722:2162-6634 7669:75-131547 7624:(7 pages) 7000:(2015) . 6958:(1965) . 6333:algorithm 6270:IBM PC AT 6181:in TBCD. 6169:– 1) + 1 6070:telephony 6022:F1 F2 F3 5907:underflow 5586:talk page 5273:Power ISA 5158:(B,8,2,1) 5112:from the 4943:Zilog Z80 4881:code page 4080:Unsigned 2422:O'Brien I 2356:Petherick 204:long mode 67:systems, 61:computing 9255:Archived 9160:(1974). 9126:Archived 9122:77-90165 8996:Archived 8956:Archived 8893:Archived 8815:Archived 8780:Archived 8705:sign bit 8686:halfbyte 8666:Archived 8628:Archived 8594:Archived 8555:Archived 8446:89-77320 8341:Archived 8337:40879271 8217:(1 page) 8138:51657314 8036:Archived 7985:Archived 7971:5776493M 7955:59015055 7846:Archived 7761:Archived 7738:51674710 7622:: 13–19. 7579:Archived 7407:Archived 7150:62-14511 6984:65-14624 6824:73-80607 6660:Archived 6597:Archived 6418:tetrades 6343:See also 6260:in many 6137:1 1 1 1 6129:1 1 1 0 6121:1 1 0 1 6113:1 1 0 0 6105:1 0 1 1 6097:1 0 1 0 6089:8 4 2 1 6049:F1 F2 F3 5951:No sign 5947:Unsigned 5941:Example 5911:overflow 5903:infinity 5876:systems. 5810:Rounding 5520:>> 5502:>> 5367:uint32_t 5355:uint32_t 5346:uint32_t 5337:uint32_t 5250:IBM 1130 5216:IBM 7074 5212:IBM 7072 5208:IBM 7070 5154:(11,8,3) 5116:through 5108:through 5088:through 5072:through 5035:IBM 1620 4913:addition 4907:Addition 4883:setting. 3937:), each 3911:Shifting 3844:Unpacked 3539:IBM 1401 3533:IBM 7080 3478:Excess-3 3175:Kautz II 2486:5-cyclic 1115:Excess-6 1049:Excess-3 443:Excess-3 121:tetrades 113:Excess-3 104:unpacked 9220:(ed.). 8508:. 1985. 8487:. 1983. 7479:code II 7136:(ed.). 6986:. 0978. 6584:Intel. 6533:Stibitz 6430:Chen–Ho 6366:Bitmask 6082:Decimal 6001:1 F2 F3 5723:scholar 5261:IBM Db2 5248:On the 5243:numeric 5146:(B,A,1) 4959:minuend 4957:to the 4871: 4868: 4865: 4859: 4856: 4842: 4839: 4836: 4830: 4827: 4813: 4810: 4807: 4801: 4798: 4784: 4781: 4778: 4772: 4769: 4755: 4752: 4749: 4743: 4740: 4726: 4723: 4720: 4714: 4711: 4697: 4694: 4691: 4685: 4682: 4668: 4665: 4662: 4656: 4653: 4639: 4636: 4633: 4627: 4624: 4610: 4607: 4598: 4595: 4346: 4314: 4156:Unicode 4116:⁠ 4104:⁠ 4064: 4016: 4000: 3915:masking 3553: 3549: 3545: 3527:IBM 705 3521:IBM 702 3514: 3510: 3506: 3497: 3493: 3489: 3474:Stibitz 3468: 3464: 3460: 3443: 3439: 3435: 3429: 3425: 3421: 3415:decimal 3114:Kautz I 2424:(Watts) 848:Decimal 535: 9 532: 8 529: 7 526: 6 523: 5 520: 4 517: 3 514: 2 511: 1 508: 0 81:decimal 9317: 9247: 9197: 9176: 9120: 9110: 9078:63, 72 9069:, 8852: 8444: 8434: 8395: 8387: 8335: 8249: 8200: 8136: 8128: 8088:(RAE). 8064:(RAE). 7977: 7969: 7961: 7953: 7945: 7935: 7896: 7736: 7728: 7720: 7704:(10). 7675: 7667: 7657: 7526: 7483:Berger 7475:code I 7421:Fig. 4 7403:I.R.E. 7363: 7289: 7279: 7162:code ( 7148: 7088: 6982: 6931: 6897: 6851: 6822: 6812: 6780: 6747: 6718: 6675: 6652: 6555:, see 6420:and 6 6326:patent 6316:, the 6266:MC6818 6084:digit 5978:F1 F2 5958:F1 F2 5953:nibble 5913:, and 5861:Adders 5836:binary 5725: 5718: 5711: 5704: 5696: 5532:return 5340:BCDadd 5304:, the 5269:POWER6 5214:, and 5199:, and 5142:(12,1) 4941:, the 4343:~ (*) 4317:\ (*) 4311:{ (*) 3984:Notes 3973:digit 3955:EBCDIC 3939:nibble 3904:012345 3854:nibble 3850:Packed 3566:EBCDIC 3485:or BCD 3453:Digit 3451: 3357: 3340: 3328: 3319: 3313: 3307: 3301: 3279: 3270: 3264: 3252: 3246: 3240: 3224: 3215: 3206: 3194: 3188: 3179: 3160: 3151: 3142: 3130: 3124: 3121: 3036: 3033: 3030: 3003: 3000: 2997: 2978: 2966: 2954: 2942: 2939: 2936: 2911: 2896: 2881: 2878: 2875: 2872: 2791: 2788: 2770: 2764: 2749: 2746: 2726: 2720: 2705: 2702: 2696: 2681: 2649: 2646: 2640: 2637: 2631: 2628: 2612:Lippel 2588: 2585: 2579: 2576: 2570: 2567: 2535: 2529: 2526: 2511: 2505: 2502: 2474: 2468: 2465: 2450: 2444: 2441: 2408: 2399: 2387: 2384: 2375: 2363: 2336: 2333: 2327: 2312: 2309: 2303: 2275: 2272: 2266: 2251: 2248: 2242: 2212: 2203: 2200: 2191: 2188: 2179: 2157: 2151: 2145: 2142: 2139: 2136: 2108:Ledley 2096: 2093: 2090: 2084: 2081: 2078: 2045:Glixon 1966: 1963: 1954: 1951: 1945: 1921: 1905: 1902: 1899: 1896: 1893: 1860: 1796: 1779: 1773: 1767: 1758: 1752: 1746: 1721: 1715: 1709: 1697: 1691: 1685: 1661: 1658: 1646: 1637: 1634: 1622: 1597: 1594: 1591: 1573: 1570: 1567: 1539: 1533: 1530: 1515: 1509: 1506: 1478: 1475: 1472: 1454: 1451: 1448: 1411: 1408: 1399: 1396: 1387: 1384: 1342: 1339: 1336: 1333: 1324: 1321: 1285: 1282: 1279: 1276: 1273: 1270: 1204: 1201: 1198: 1195: 1192: 1189: 1117:(XS-6) 1051:(XS-3) 1020: 1017: 1014: 1011: 1008: 1005: 969: 966: 963: 960: 957: 945: 616:Binary 505:Weight 192:per se 179:, the 126:nibble 108:packed 77:binary 9352:. 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