1704:
693:
1699:{\displaystyle {\begin{aligned}\operatorname {NOT} x&=\sum _{n=0}^{\lfloor \log _{2}(x)\rfloor }2^{n}\left=2^{\left\lfloor \log _{2}(x)\right\rfloor +1}-1-x\\x\operatorname {AND} y&=\sum _{n=0}^{\lfloor \log _{2}(x)\rfloor }2^{n}\left(\left\lfloor {\frac {x}{2^{n}}}\right\rfloor {\bmod {2}}\right)\left(\left\lfloor {\frac {y}{2^{n}}}\right\rfloor {\bmod {2}}\right)\\x\operatorname {OR} y&=\sum _{n=0}^{\lfloor \log _{2}(x)\rfloor }2^{n}\left(\left(\left\lfloor {\frac {x}{2^{n}}}\right\rfloor {\bmod {2}}\right)+\left(\left\lfloor {\frac {y}{2^{n}}}\right\rfloor {\bmod {2}}\right)-\left(\left\lfloor {\frac {x}{2^{n}}}\right\rfloor {\bmod {2}}\right)\left(\left\lfloor {\frac {y}{2^{n}}}\right\rfloor {\bmod {2}}\right)\right)\\x\operatorname {XOR} y&=\sum _{n=0}^{\lfloor \log _{2}(x)\rfloor }2^{n}\left(\left{\bmod {2}}\right)=\sum _{n=0}^{\lfloor \log _{2}(x)\rfloor }2^{n}\left\end{aligned}}}
476:
2268:
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2479:
2375:
2365:
2260:
36:
2447:
2605:, so care must be taken when using them. The result of shifting by a bit count greater than or equal to the word's size is undefined behavior in C and C++. Right-shifting a negative value is implementation-defined and not recommended by good coding practice; the result of left-shifting a signed value is undefined if the result cannot be represented in the result type.
2437:
271:
403:
2462:, the bits are "rotated" as if the left and right ends of the register were joined. The value that is shifted into the right during a left-shift is whatever value was shifted out on the left, and vice versa for a right-shift operation. This is useful if it is necessary to retain all the existing bits, and is frequently used in digital
2538:, because if a large number is stored in two registers, the bit that is shifted off one end of the first register must come in at the other end of the second. With rotate-through-carry, that bit is "saved" in the carry flag during the first shift, ready to shift in during the second shift without any extra preparation.
514:
The bitwise XOR may be used to invert selected bits in a register (also called toggle or flip). Any bit may be toggled by XORing it with 1. For example, given the bit pattern 0010 (decimal 2) the second and fourth bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the second and
2833:
where the shift amount is tested to ensure that it does not introduce undefined behavior. However, the branch adds an additional code path and presents an opportunity for timing analysis and attack, which is often not acceptable in high-integrity software. In addition, the code compiles to multiple
2191:
If the width of the register (frequently 32 or even 64) is larger than the number of bits (usually 8) of the smallest addressable unit, frequently called byte, the shift operations induce an addressing scheme from the bytes to the bits. Thereby the orientations "left" and "right" are taken from the
174:
On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due
3036:
If the promoted type of the left-hand operand is int, only the five lowest-order bits of the right-hand operand are used as the shift distance. It is as if the right-hand operand were subjected to a bitwise logical AND operator & with the mask value 0x1f (0b11111). The shift distance actually
365:
For example, 0110 (decimal 6) can be considered a set of four flags numbered from right to left, where the first and fourth flags are clear (0), and the second and third flags are set (1). The third flag may be cleared by using a bitwise AND with the pattern that has a zero only in the third bit:
3040:
If the promoted type of the left-hand operand is long, then only the six lowest-order bits of the right-hand operand are used as the shift distance. It is as if the right-hand operand were subjected to a bitwise logical AND operator & with the mask value 0x3f (0b111111). The shift distance
3644:
It can be hard to solve for variables in
Boolean algebra, because unlike regular algebra, several operations do not have inverses. Operations without inverses lose some of the original data bits when they are performed, and it is not possible to recover this missing information.
2182:
in a computer processor have a fixed width, so some bits will be "shifted out" of the register at one end, while the same number of bits are "shifted in" from the other end; the differences between bit shift operators lie in how they determine the values of the shifted-in bits.
495:
operation on each pair of corresponding bits. The result in each position is 1 if only one of the bits is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same. For example:
262:, which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a decreasing range from 255 to 0. A simple but illustrative example use is to invert a grayscale image where each pixel is stored as an unsigned integer.
294:
operation on each pair of the corresponding bits. Thus, if both bits in the compared position are 1, the bit in the resulting binary representation is 1 (1 × 1 = 1); otherwise, the result is 0 (1 × 0 = 0 and 0 × 0 = 0). For example:
191:
In the explanations below, any indication of a bit's position is counted from the right (least significant) side, advancing left. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first (i.e., the rightmost) one.
2200:
orientation. Disregarding the boundary effects at both ends of the register, arithmetic and logical shift operations behave the same, and a shift by 8 bit positions transports the bit pattern by 1 byte position in the following way:
3220:
Although machines often have efficient built-in instructions for performing arithmetic and logical operations, all these operations can be performed by combining the bitwise operators and zero-testing in various ways. For example, here is a
440:
The bitwise OR may be used to set to 1 the selected bits of the register described above. For example, the fourth bit of 0010 (decimal 2) may be set by performing a bitwise OR with the pattern with only the fourth bit set:
2503:
is a variant of the rotate operation, where the bit that is shifted in (on either end) is the old value of the carry flag, and the bit that is shifted out (on the other end) becomes the new value of the carry flag.
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However, as the logical right-shift inserts value 0 bits into the most significant bit, instead of copying the sign bit, it is ideal for unsigned binary numbers, while the arithmetic right-shift is ideal for signed
558:
to zero. Performing XOR on a value against itself always yields zero, and on many architectures this operation requires fewer clock cycles and less memory than loading a zero value and saving it to the register.
2303:
In the first case, the leftmost digit was shifted past the end of the register, and a new 0 was shifted into the rightmost position. In the second case, the rightmost 1 was shifted out (perhaps into the
698:
2308:), and a new 1 was copied into the leftmost position, preserving the sign of the number. Multiple shifts are sometimes shortened to a single shift by some number of digits. For example:
258:, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. For example, for 8-bit unsigned integers,
611:
321:(0). For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit:
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are sometimes considered bitwise operations, because they treat a value as a series of bits rather than as a numerical quantity. In these operations, the digits are moved, or
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Bitwise operations are necessary particularly in lower-level programming such as device drivers, low-level graphics, communications protocol packet assembly, and decoding.
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In C#, the right-shift is an arithmetic shift when the first operand is an int or long. If the first operand is of type uint or ulong, the right-shift is a logical shift.
683:
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Sometimes it is useful to simplify complex expressions made up of bitwise operations, for example when writing compilers. The goal of a compiler is to translate a
2947:. Clang provides some rotate intrinsics for Microsoft compatibility that suffers the problems above. GCC does not offer rotate intrinsics. Intel also provides x86
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behaves like a logical shift, and does not copy the sign bit. The number of places to shift is given as the second argument. For example, the following assigns
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Throughout this article, 0xFFFF means that all the bits in your data type need to be set to 1. The exact number of bits depends on the width of the data type.
2279:, the bits that are shifted out of either end are discarded. In a left arithmetic shift, zeros are shifted in on the right; in a right arithmetic shift, the
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can simulate a logical or arithmetic shift of one position by setting up the carry flag beforehand. For example, if the carry flag contains 0, then
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422:
operation on each pair of corresponding bits. The result in each position is 0 if both bits are 0, while otherwise the result is 1. For example:
351:, portions that should not be altered or portions that are not of interest. In this case, the 0 values mask the bits that are not of interest.)
2975:" to perform logical right shifts, but since the logical and arithmetic left-shift operations are identical for signed integer, there is no "
2196:, such that a left shift increases and a right shift decreases the value of the number ― if the left digits are read first, this makes up a
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53:
2845:, the following is recommended. The pattern is recognized by many compilers, and the compiler will emit a single rotate instruction:
119:
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100:
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3226:
2390:, zeros are shifted in to replace the discarded bits. Therefore, the logical and arithmetic left-shifts are exactly the same.
72:
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57:
3989:"Constant not propagated into inline assembly, results in "constraint 'I' expects an integer constant expression""
2624:), but one can be synthesized from the shift operators. Care must be taken to ensure the statement is well formed to avoid
2948:
171:. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands.
79:
3849:
567:
3071:. If the byte value is negative, the highest bit is one, then ones are used to fill up the extra bytes in the int. So
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in software with security requirements. For example, a naive implementation that left-rotates a 32-bit unsigned value
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255:
86:
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Because the result 0010 is non-zero, we know the second bit in the original pattern was set. This is often called
46:
167:. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the
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3690:
2565:" for right shift. The number of places to shift is given as the second argument to the operator. For example,
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Rotate through carry is especially useful when performing shifts on numbers larger than the processor's native
68:
362:. This technique is an efficient way to store a number of Boolean values using as little memory as possible.
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Another example is a pseudocode implementation of addition, showing how to calculate a sum of two integers
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133:
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design choices, bitwise operations do commonly use less power because of the reduced use of resources.
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3695:
Operations at the top of this list are executed first. See the main article for a more complete list.
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of the given binary value. Bits that are 0 become 1, and those that are 1 become 0. For example:
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The type of the shift expression is the promoted type of the left-hand operand. For example,
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machine instructions, which is often less efficient than the processor's native instruction.
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of a binary number by checking the value of the lowest valued bit. Using the example above:
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This technique may be used to manipulate bit patterns representing sets of
Boolean states.
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is a logical right-shift, and if the carry flag contains a copy of the sign bit, then
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is an arithmetic right-shift. For this reason, some microcontrollers such as low end
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687:, for the non-negative integers, the bitwise operations can be written as follows:
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Additionally, XOR can be composed using the 3 basic operations (AND, OR, NOT)
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possible. Boolean algebra is used to simplify complex bitwise expressions.
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The C-family of languages lack a rotate operator (although C++20 provides
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to the left by two bits, which is equivalent to a multiplication by four.
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This example uses an 8-bit register, interpreted as two's complement:
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of the value minus one. If two's complement arithmetic is used, then
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that takes two equal-length binary representations and performs the
4115:
2342:, then the same right-shift operation results in division by 2 and
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Because 6 AND 1 is zero, 6 is divisible by two and therefore even.
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The operation may be used to determine whether a particular bit is
3041:
actually used is therefore always in the range 0 to 63, inclusive.
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2739:
is outside the range 0–31 inclusive. A second try might result in
2531:, and don't bother with arithmetic or logical shift instructions.
617:
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269:
3923:"Near constant time rotate that does not violate the standards?"
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bits results in undefined behavior in the right-hand expression
2971:" operators perform arithmetic shifts. Java adds the operator "
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is equivalent to multiplying by 2 (provided the value does not
1729:
Here is the bitwise equivalent operations of two bits P and Q:
4059:"Synthesizing arithmetic operations using bit-shifting tricks"
2240:
a right shift by 8 positions increases the byte address by 1.
2222:
a right shift by 8 positions decreases the byte address by 1.
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29:
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a left shift by 8 positions decreases the byte address by 1,
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a left shift by 8 positions increases the byte address by 1,
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that takes two bit patterns of equal length and performs the
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that takes two bit patterns of equal length and performs the
3880:. Software Engineering Institute, Carnegie Mellon University
163:(considered as a bit string) at the level of its individual
2473:
2431:
2359:
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sometimes use XOR as a short-cut to setting the value of a
391:
0110 (decimal 6) AND 0001 (decimal 1) = 0000 (decimal 0)
358:) of a register in which each bit represents an individual
3874:"INT13-C. Use bitwise operators only on unsigned operands"
132:"Binary shift" redirects here. For the excess-3 code, see
3037:
used is therefore always in the range 0 to 31, inclusive.
2557:
In C and C++ languages, the logical shift operators are "
4141:" by Enrique Zeleny, The Wolfram Demonstrations Project.
3129:
uses bitwise operations to evaluate each of two or more
2601:
Shifts can result in implementation-defined behavior or
3965:"Circular rotate that does not violate C/C++ standard?"
649:, then vector addition corresponds to the bitwise XOR.
384:
Because of this property, it becomes easy to check the
354:
The bitwise AND may be used to clear selected bits (or
240:
NOT 10101011 (decimal 171) = 01010100 (decimal 84)
2338:
of division by 2. If the binary number is treated as
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665:
623:
583:
3149:), the logical left and right shift operators are "
3141:In Pascal, as well as in all its dialects (such as
3114:
3072:
3045:
3010:
2837:To avoid the undefined behavior and branches under
60:. Unsourced material may be challenged and removed.
2548:Circular shift § Implementing circular shifts
2311:00010111 (decimal +23) LEFT-SHIFT-BY-TWO = 010111
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640:
605:
3691:Operators in C and C++ § Operator precedence
3917:
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3229:showing how to multiply two arbitrary integers
4019:
4017:
8:
3944:"Poor optimization of portable rotate idiom"
3837:JTC1/SC22/WG14 N843 "C programming language"
2289:00010111 (decimal +23) LEFT-SHIFT = 0010111
1710:Truth table for all binary logical operators
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4139:Plots Of Compositions Of Bitwise Operations
3624:x & (y ^ z) = (x & y) ^ (x & z)
3619:x & (y | z) = (x & y) | (x & z)
3157:", respectively. Even for signed integers,
3629:x + y = (x ^ y) + ((x & y) << 1)
3356:using bitwise operators and zero-testing:
562:If the set of bit strings of fixed length
4008:The Java Language Specification, section
3850:"Arithmetic operators - cppreference.com"
3469:x & (y & z) = (x & y) & z
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120:Learn how and when to remove this message
2963:, all integer types are signed, so the "
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3614:x | (y & z) = (x | y) & (x | z)
2296:10010111 (decimal −105) RIGHT-SHIFT =
4118:, a tool for bitwise-XOR files/streams
3983:
3981:
3059:In bit and shift operations, the type
2998:(unsigned right shift) are called the
2982:More details of Java shift operators:
3245:) using only bitshifts and addition:
2326:), while a right arithmetic shift by
7:
3832:
3830:
2458:In this operation, sometimes called
58:adding citations to reliable sources
4096:- is subtraction here, not negation
4087:- is negation here, not subtraction
3582:a ^ b = (a & ~b) | (~a & b)
2517:x RIGHT-ROTATE-THROUGH-CARRY-BY-ONE
2513:x RIGHT-ROTATE-THROUGH-CARRY-BY-ONE
3056:bit positions with zero-extension.
2334:value is equivalent to taking the
25:
3814:"CMicrotek Low-power Design Blog"
2927:There are also compiler-specific
2192:standard writing of numbers in a
606:{\displaystyle {\bf {F}}_{2}^{n}}
4112:supports Bitwise AND, OR and XOR
627:
587:
34:
3577:a ^ b = (a | b) & (~a | ~b)
3448:high-level programming language
3227:ancient Egyptian multiplication
136:. For the general concept, see
45:needs additional citations for
4132:Wolfram Demonstrations Project
3640:Inverses and solving equations
2450:Right circular shift or rotate
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1409:
1403:
1134:
1128:
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1:
3878:CERT: Secure Coding Standards
2440:Left circular shift or rotate
2412:Another form of shift is the
641:{\displaystyle {\bf {F}}_{2}}
479:Bitwise XOR of 4-bit integers
4061:. Bisqwit.iki.fi. 2014-02-15
406:Bitwise OR of 4-bit integers
3065:is implicitly converted to
2318:A left arithmetic shift by
550:programmers and optimizing
243:The result is equal to the
4181:
3688:
3439:
2994:(signed right shift), and
2545:
2492:Right rotate through carry
2405:
2353:
2252:
343:. (By analogy, the use of
199:
131:
4110:Online Bitwise Calculator
4025:"Chapter 15. Expressions"
3899:"Operator (C# Reference)"
3547:x ^ (y ^ z) = (x ^ y) ^ z
3503:x | (y | z) = (x | y) | z
3169:to the left by two bits:
2482:Left rotate through carry
2058:
1790:
1744:
222:on each bit, forming the
4128:Bitwise Operations Mod N
4122:Division using bitshifts
3967:. Intel Developer Forums
3925:. Stack Exchange Network
3450:into the most efficient
3358:
3247:
3171:
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2741:
2642:
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2553:In C family of languages
2178:, to the left or right.
653:Mathematical equivalents
4160:Operators (programming)
3763:Bitwise operations in C
3165:the result of shifting
2594:the result of shifting
2542:In high-level languages
678:{\displaystyle x\geq y}
4010:15.19. Shift Operators
3609:~(x & y) = ~x | ~y
3604:~(x | y) = ~x & ~y
3203:, used in cryptography
2561:" for left shift and "
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2300:1001011 (decimal −53)
2272:
2271:Right arithmetic shift
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1714:There are 16 possible
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570:) is thought of as an
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279:
27:Computer science topic
4130:" by Enrique Zeleny,
3748:Arithmetic logic unit
3464:x & y = y & x
2725:(x >> (32 - n))
2546:Further information:
2491:
2481:
2449:
2439:
2406:Further information:
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2263:Left arithmetic shift
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377:11 (decimal 11) = 0
273:
233:111 (decimal 7) =
177:instruction pipelines
134:Shifted binary (code)
4042:"JavaScript Bitwise"
3007:aByte >>> 2
2979:" operator in Java.
2719:However, a shift by
2640:positions is simply
2529:rotate through carry
2509:rotate through carry
2501:Rotate through carry
2470:Rotate through carry
2344:rounding toward zero
2194:place-value notation
694:
663:
621:
581:
493:logical exclusive OR
420:logical inclusive OR
373:10 (decimal 6) AND 1
332:0 (decimal 2) = 00
328:1 (decimal 3) AND 00
145:computer programming
54:improve this article
3854:en.cppreference.com
3793:Primitive data type
3685:Order of operations
3599:x & (x | y) = x
3594:x | (x & y) = x
3513:x | 0xFFFF = 0xFFFF
3207:count leading zeros
2378:Right logical shift
602:
533:0 (decimal 10) =
507:1 (decimal 3) = 0
503:1 (decimal 5) XOR 0
306:(decimal 3) = 000
302:(decimal 5) AND 001
69:"Bitwise operation"
3474:x & 0xFFFF = x
3225:implementation of
2626:undefined behavior
2603:undefined behavior
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2368:Left logical shift
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525:0 (decimal 2) XOR
515:fourth positions:
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212:bitwise complement
4155:Binary arithmetic
3946:. GNU GCC Project
3720:<< >>
3634:x - y = ~(~x + y)
3009:is equivalent to
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548:Assembly language
459:0 (decimal 8) =
451:0 (decimal 2) OR
237:000 (decimal 8)
187:Bitwise operators
149:bitwise operation
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16:(Redirected from
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3940:
3934:
3933:
3931:
3930:
3919:
3910:
3909:
3907:
3906:
3895:
3889:
3888:
3886:
3885:
3870:
3864:
3863:
3861:
3860:
3846:
3840:
3834:
3825:
3824:
3822:
3821:
3810:
3788:Logical operator
3753:Bit manipulation
3736:
3731:
3726:
3721:
3716:
3711:
3706:
3701:
3635:
3630:
3625:
3620:
3615:
3610:
3605:
3600:
3595:
3583:
3578:
3568:
3563:
3558:
3553:
3548:
3543:
3531:
3519:
3514:
3509:
3504:
3499:
3487:
3480:
3475:
3470:
3465:
3431:
3428:
3425:
3422:
3419:
3416:
3413:
3410:
3407:
3404:
3401:
3398:
3395:
3392:
3389:
3386:
3383:
3380:
3377:
3374:
3371:
3368:
3365:
3362:
3355:
3351:
3344:
3341:
3338:
3335:
3332:
3329:
3326:
3323:
3320:
3317:
3314:
3311:
3308:
3305:
3302:
3299:
3296:
3293:
3290:
3287:
3284:
3281:
3278:
3275:
3272:
3269:
3266:
3263:
3260:
3257:
3254:
3251:
3244:
3240:
3236:
3232:
3190:
3187:
3184:
3181:
3178:
3175:
3160:
3156:
3152:
3116:
3112:
3111:
3108:
3105:
3102:
3099:
3096:
3093:
3090:
3087:
3084:
3081:
3078:
3075:
3070:
3064:
3047:
3046:n >>> s
3032:
3031:
3028:
3025:
3022:
3019:
3016:
3013:
3008:
2997:
2993:
2989:
2978:
2974:
2970:
2966:
2923:
2920:
2917:
2914:
2911:
2908:
2905:
2902:
2899:
2896:
2893:
2890:
2887:
2884:
2881:
2878:
2875:
2872:
2869:
2866:
2863:
2860:
2857:
2854:
2851:
2829:
2826:
2823:
2820:
2817:
2814:
2811:
2808:
2805:
2802:
2799:
2796:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2772:
2769:
2766:
2763:
2760:
2757:
2754:
2751:
2748:
2745:
2738:
2734:
2730:
2726:
2722:
2715:
2712:
2709:
2706:
2703:
2700:
2697:
2694:
2691:
2688:
2685:
2682:
2679:
2676:
2673:
2670:
2667:
2664:
2661:
2658:
2655:
2652:
2649:
2646:
2639:
2635:
2623:
2619:
2597:
2593:
2586:
2583:
2580:
2577:
2574:
2571:
2564:
2560:
2518:
2514:
2474:
2432:
2418:bitwise rotation
2398:binary numbers.
2396:two's complement
2360:
2340:ones' complement
2332:two's complement
2277:arithmetic shift
2255:Arithmetic shift
2249:Arithmetic shift
2206:
2205:
2157:
2152:
2145:
2140:
2133:
2128:
2121:
2116:
2109:
2104:
2097:
2090:
2083:
2076:
2069:
2064:
1732:
1720:binary variables
1705:
1703:
1702:
1697:
1695:
1691:
1687:
1686:
1685:
1676:
1672:
1671:
1667:
1665:
1664:
1652:
1643:
1639:
1637:
1636:
1624:
1608:
1607:
1597:
1581:
1580:
1567:
1549:
1545:
1544:
1543:
1534:
1530:
1529:
1525:
1524:
1523:
1514:
1510:
1508:
1507:
1495:
1481:
1477:
1476:
1475:
1466:
1462:
1460:
1459:
1447:
1426:
1425:
1415:
1399:
1398:
1385:
1347:
1343:
1342:
1338:
1337:
1336:
1327:
1323:
1321:
1320:
1308:
1297:
1293:
1292:
1291:
1282:
1278:
1276:
1275:
1263:
1249:
1245:
1244:
1243:
1234:
1230:
1228:
1227:
1215:
1201:
1197:
1196:
1195:
1186:
1182:
1180:
1179:
1167:
1151:
1150:
1140:
1124:
1123:
1110:
1072:
1068:
1067:
1066:
1057:
1053:
1051:
1050:
1038:
1027:
1023:
1022:
1021:
1012:
1008:
1006:
1005:
993:
982:
981:
971:
955:
954:
941:
891:
890:
883:
879:
866:
865:
843:
839:
838:
837:
828:
824:
817:
816:
807:
803:
801:
800:
788:
772:
771:
761:
745:
744:
731:
686:
684:
682:
681:
676:
647:
645:
644:
639:
637:
636:
631:
630:
612:
610:
609:
604:
601:
596:
591:
590:
489:binary operation
433:(decimal 3) = 0
429:(decimal 5) OR 0
416:binary operation
288:binary operation
261:
250:
245:two's complement
224:ones' complement
220:logical negation
202:Ones' complement
175:to their longer
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
4180:
4179:
4175:
4174:
4173:
4171:
4170:
4169:
4165:Boolean algebra
4145:
4144:
4106:
4101:
4100:
4095:
4091:
4086:
4082:
4077:
4073:
4064:
4062:
4057:
4056:
4052:
4040:
4036:
4023:
4022:
4015:
4007:
4003:
3994:
3992:
3987:
3986:
3979:
3970:
3968:
3963:
3962:
3958:
3949:
3947:
3942:
3941:
3937:
3928:
3926:
3921:
3920:
3913:
3904:
3902:
3897:
3896:
3892:
3883:
3881:
3872:
3871:
3867:
3858:
3856:
3848:
3847:
3843:
3839:, section 6.5.7
3835:
3828:
3819:
3817:
3812:
3811:
3807:
3802:
3797:
3743:
3734:
3729:
3724:
3719:
3714:
3709:
3704:
3699:
3693:
3687:
3642:
3633:
3628:
3623:
3618:
3613:
3608:
3603:
3598:
3593:
3590:
3581:
3576:
3567:x ^ 0xFFFF = ~x
3566:
3561:
3556:
3551:
3546:
3541:
3538:
3529:
3526:
3517:
3512:
3507:
3502:
3497:
3494:
3485:
3478:
3473:
3468:
3463:
3460:
3444:
3442:Boolean algebra
3438:
3436:Boolean algebra
3433:
3432:
3429:
3426:
3423:
3420:
3417:
3414:
3411:
3408:
3405:
3402:
3399:
3396:
3393:
3390:
3387:
3384:
3381:
3378:
3375:
3372:
3369:
3366:
3363:
3360:
3353:
3349:
3346:
3345:
3342:
3339:
3336:
3333:
3330:
3327:
3324:
3321:
3318:
3315:
3312:
3309:
3306:
3303:
3300:
3297:
3294:
3291:
3288:
3285:
3282:
3279:
3276:
3273:
3270:
3267:
3264:
3261:
3258:
3255:
3252:
3249:
3242:
3238:
3234:
3230:
3215:
3197:
3192:
3191:
3188:
3185:
3182:
3179:
3176:
3173:
3158:
3154:
3150:
3147:Standard Pascal
3139:
3124:
3113:will result in
3109:
3106:
3103:
3100:
3097:
3094:
3091:
3088:
3085:
3082:
3079:
3076:
3073:
3066:
3060:
3029:
3026:
3023:
3020:
3017:
3014:
3011:
3006:
3000:shift operators
2995:
2991:
2987:
2976:
2972:
2968:
2964:
2957:
2941:_rotr8, _rotr16
2937:_rotl8, _rotl16
2933:circular shifts
2925:
2924:
2921:
2918:
2915:
2912:
2909:
2906:
2903:
2900:
2897:
2894:
2891:
2888:
2885:
2882:
2879:
2876:
2873:
2870:
2867:
2864:
2861:
2858:
2855:
2852:
2849:
2831:
2830:
2827:
2824:
2821:
2818:
2815:
2812:
2809:
2806:
2803:
2800:
2797:
2794:
2791:
2788:
2785:
2782:
2779:
2776:
2773:
2770:
2767:
2764:
2761:
2758:
2755:
2752:
2749:
2746:
2743:
2736:
2732:
2728:
2724:
2720:
2717:
2716:
2713:
2710:
2707:
2704:
2701:
2698:
2695:
2692:
2689:
2686:
2683:
2680:
2677:
2674:
2671:
2668:
2665:
2662:
2659:
2656:
2653:
2650:
2647:
2644:
2637:
2633:
2621:
2617:
2614:
2612:Circular shifts
2595:
2591:
2588:
2587:
2584:
2581:
2578:
2575:
2572:
2569:
2562:
2558:
2555:
2550:
2544:
2516:
2512:
2472:
2460:rotate no carry
2430:
2410:
2404:
2358:
2352:
2316:
2301:
2294:
2257:
2251:
2189:
2168:
2147:
2135:
2123:
2111:
2099:
2092:
2085:
2078:
2071:
2060:
1716:truth functions
1712:
1693:
1692:
1656:
1647:
1628:
1619:
1618:
1614:
1613:
1609:
1599:
1572:
1499:
1490:
1489:
1485:
1451:
1442:
1441:
1437:
1436:
1432:
1431:
1427:
1417:
1390:
1364:
1349:
1348:
1312:
1303:
1302:
1298:
1267:
1258:
1257:
1253:
1219:
1210:
1209:
1205:
1171:
1162:
1161:
1157:
1156:
1152:
1142:
1115:
1089:
1074:
1073:
1042:
1033:
1032:
1028:
997:
988:
987:
983:
973:
946:
920:
905:
904:
857:
856:
852:
847:
792:
783:
782:
778:
777:
773:
763:
736:
710:
692:
691:
661:
660:
658:
655:
624:
619:
618:
579:
578:
542:
512:
473:
468:
467:0 (decimal 10)
438:
400:
392:
382:
381:10 (decimal 2)
337:
311:
274:Bitwise AND of
268:
260:NOT x = 255 - x
259:
248:
241:
238:
216:unary operation
204:
198:
189:
141:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
4178:
4176:
4168:
4167:
4162:
4157:
4147:
4146:
4143:
4142:
4135:
4124:
4119:
4113:
4105:
4104:External links
4102:
4099:
4098:
4089:
4080:
4071:
4050:
4034:
4013:
4001:
3991:. LLVM Project
3977:
3956:
3935:
3911:
3890:
3865:
3841:
3826:
3804:
3803:
3801:
3798:
3796:
3795:
3790:
3785:
3780:
3775:
3773:Find first set
3770:
3765:
3760:
3755:
3750:
3744:
3742:
3739:
3738:
3737:
3732:
3727:
3722:
3717:
3712:
3707:
3702:
3689:Main article:
3686:
3683:
3682:
3681:
3680:
3679:
3676:
3673:
3670:
3664:
3663:
3662:
3659:
3656:
3653:
3641:
3638:
3637:
3636:
3631:
3626:
3621:
3616:
3611:
3606:
3601:
3596:
3589:
3586:
3585:
3584:
3579:
3570:
3569:
3564:
3559:
3554:
3549:
3544:
3537:
3534:
3533:
3532:
3525:
3522:
3521:
3520:
3515:
3510:
3505:
3500:
3493:
3490:
3489:
3488:
3482:
3481:
3476:
3471:
3466:
3459:
3456:
3440:Main article:
3437:
3434:
3359:
3248:
3214:
3211:
3210:
3209:
3204:
3196:
3193:
3172:
3138:
3135:
3123:
3120:
3119:
3118:
3057:
3052:right-shifted
3042:
3038:
3034:
3003:
2990:(left shift),
2986:The operators
2956:
2953:
2848:
2742:
2643:
2630:timing attacks
2613:
2610:
2568:
2554:
2551:
2543:
2540:
2496:
2495:
2485:
2471:
2468:
2454:
2453:
2443:
2429:
2426:
2414:circular shift
2408:Circular shift
2403:
2402:Circular shift
2400:
2382:
2381:
2371:
2354:Main article:
2351:
2348:
2315:(decimal +92)
2310:
2295:
2293:(decimal +46)
2288:
2253:Main article:
2250:
2247:
2246:
2245:
2242:
2241:
2238:
2235:
2234:
2231:
2224:
2223:
2220:
2217:
2216:
2213:
2188:
2187:Bit addressing
2185:
2167:
2164:
2161:
2160:
2155:
2150:
2143:
2138:
2131:
2126:
2119:
2114:
2107:
2102:
2095:
2088:
2081:
2074:
2067:
2062:
2056:
2055:
2052:
2049:
2046:
2043:
2040:
2037:
2034:
2031:
2028:
2025:
2022:
2019:
2016:
2013:
2010:
2007:
2004:
2000:
1999:
1996:
1993:
1990:
1987:
1984:
1981:
1978:
1975:
1972:
1969:
1966:
1963:
1960:
1957:
1954:
1951:
1948:
1944:
1943:
1940:
1937:
1934:
1931:
1928:
1925:
1922:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1895:
1892:
1888:
1887:
1884:
1881:
1878:
1875:
1872:
1869:
1866:
1863:
1860:
1857:
1854:
1851:
1848:
1845:
1842:
1839:
1836:
1832:
1831:
1826:
1821:
1816:
1811:
1806:
1801:
1796:
1791:
1789:
1784:
1779:
1772:
1767:
1760:
1755:
1750:
1745:
1743:
1738:
1711:
1708:
1707:
1706:
1690:
1684:
1680:
1675:
1670:
1663:
1659:
1655:
1650:
1646:
1642:
1635:
1631:
1627:
1622:
1617:
1612:
1606:
1602:
1596:
1593:
1590:
1587:
1584:
1579:
1575:
1571:
1566:
1563:
1560:
1556:
1552:
1548:
1542:
1538:
1533:
1528:
1522:
1518:
1513:
1506:
1502:
1498:
1493:
1488:
1484:
1480:
1474:
1470:
1465:
1458:
1454:
1450:
1445:
1440:
1435:
1430:
1424:
1420:
1414:
1411:
1408:
1405:
1402:
1397:
1393:
1389:
1384:
1381:
1378:
1374:
1370:
1367:
1365:
1363:
1360:
1357:
1354:
1351:
1350:
1346:
1341:
1335:
1331:
1326:
1319:
1315:
1311:
1306:
1301:
1296:
1290:
1286:
1281:
1274:
1270:
1266:
1261:
1256:
1252:
1248:
1242:
1238:
1233:
1226:
1222:
1218:
1213:
1208:
1204:
1200:
1194:
1190:
1185:
1178:
1174:
1170:
1165:
1160:
1155:
1149:
1145:
1139:
1136:
1133:
1130:
1127:
1122:
1118:
1114:
1109:
1106:
1103:
1099:
1095:
1092:
1090:
1088:
1085:
1082:
1079:
1076:
1075:
1071:
1065:
1061:
1056:
1049:
1045:
1041:
1036:
1031:
1026:
1020:
1016:
1011:
1004:
1000:
996:
991:
986:
980:
976:
970:
967:
964:
961:
958:
953:
949:
945:
940:
937:
934:
930:
926:
923:
921:
919:
916:
913:
910:
907:
906:
903:
900:
897:
894:
889:
886:
882:
878:
875:
872:
869:
864:
860:
855:
850:
846:
842:
836:
832:
827:
823:
820:
815:
811:
806:
799:
795:
791:
786:
781:
776:
770:
766:
760:
757:
754:
751:
748:
743:
739:
735:
730:
727:
724:
720:
716:
713:
711:
709:
706:
703:
700:
699:
674:
671:
668:
654:
651:
635:
629:
600:
595:
589:
541:0 (decimal 8)
517:
511:0 (decimal 6)
498:
472:
469:
443:
424:
399:
396:
390:
368:
336:0 (decimal 2)
323:
297:
267:
264:
249:NOT x = -x − 1
239:
228:
218:that performs
197:
194:
188:
185:
161:binary numeral
151:operates on a
128:
127:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4177:
4166:
4163:
4161:
4158:
4156:
4153:
4152:
4150:
4140:
4136:
4133:
4129:
4125:
4123:
4120:
4117:
4114:
4111:
4108:
4107:
4103:
4093:
4090:
4084:
4081:
4075:
4072:
4060:
4054:
4051:
4047:
4046:W3Schools.com
4043:
4038:
4035:
4030:
4026:
4020:
4018:
4014:
4011:
4005:
4002:
3990:
3984:
3982:
3978:
3966:
3960:
3957:
3945:
3939:
3936:
3924:
3918:
3916:
3912:
3900:
3894:
3891:
3879:
3875:
3869:
3866:
3855:
3851:
3845:
3842:
3838:
3833:
3831:
3827:
3815:
3809:
3806:
3799:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3776:
3774:
3771:
3769:
3768:Double dabble
3766:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3745:
3740:
3733:
3728:
3723:
3718:
3713:
3708:
3703:
3698:
3697:
3696:
3692:
3684:
3677:
3674:
3671:
3668:
3667:
3665:
3660:
3657:
3654:
3651:
3650:
3648:
3647:
3646:
3639:
3632:
3627:
3622:
3617:
3612:
3607:
3602:
3597:
3592:
3591:
3587:
3580:
3575:
3574:
3573:
3565:
3560:
3557:x ^ y ^ y = x
3555:
3550:
3545:
3542:x ^ y = y ^ x
3540:
3539:
3535:
3528:
3527:
3523:
3516:
3511:
3506:
3501:
3498:x | y = y | x
3496:
3495:
3491:
3486:x & x = x
3484:
3483:
3479:x & 0 = 0
3477:
3472:
3467:
3462:
3461:
3457:
3455:
3453:
3449:
3443:
3435:
3357:
3246:
3241:greater than
3228:
3224:
3218:
3212:
3208:
3205:
3202:
3199:
3198:
3194:
3170:
3168:
3164:
3148:
3144:
3143:Object Pascal
3136:
3134:
3132:
3128:
3121:
3069:
3063:
3058:
3055:
3051:
3044:The value of
3043:
3039:
3035:
3004:
3001:
2985:
2984:
2983:
2980:
2962:
2954:
2952:
2950:
2946:
2943:in Microsoft
2942:
2938:
2934:
2931:implementing
2930:
2846:
2844:
2840:
2835:
2740:
2641:
2631:
2627:
2611:
2609:
2606:
2604:
2599:
2566:
2552:
2549:
2541:
2539:
2537:
2532:
2530:
2526:
2522:
2510:
2505:
2502:
2490:
2486:
2480:
2476:
2475:
2469:
2467:
2465:
2461:
2448:
2444:
2438:
2434:
2433:
2427:
2425:
2423:
2419:
2415:
2409:
2401:
2399:
2397:
2391:
2389:
2388:logical shift
2376:
2372:
2366:
2362:
2361:
2357:
2356:Logical shift
2350:Logical shift
2349:
2347:
2345:
2341:
2337:
2333:
2329:
2325:
2321:
2314:
2309:
2307:
2299:
2292:
2287:
2284:
2282:
2278:
2269:
2261:
2256:
2248:
2239:
2237:
2236:
2232:
2229:
2226:
2225:
2221:
2219:
2218:
2214:
2211:
2210:Little-endian
2208:
2207:
2204:
2203:
2202:
2199:
2195:
2186:
2184:
2181:
2177:
2173:
2165:
2156:
2151:
2144:
2139:
2132:
2127:
2120:
2115:
2108:
2103:
2096:
2089:
2082:
2075:
2068:
2063:
2057:
2053:
2050:
2047:
2044:
2041:
2038:
2035:
2032:
2029:
2026:
2023:
2020:
2017:
2014:
2011:
2008:
2005:
2002:
2001:
1997:
1994:
1991:
1988:
1985:
1982:
1979:
1976:
1973:
1970:
1967:
1964:
1961:
1958:
1955:
1952:
1949:
1946:
1945:
1941:
1938:
1935:
1932:
1929:
1926:
1923:
1920:
1917:
1914:
1911:
1908:
1905:
1902:
1899:
1896:
1893:
1890:
1889:
1885:
1882:
1879:
1876:
1873:
1870:
1867:
1864:
1861:
1858:
1855:
1852:
1849:
1846:
1843:
1840:
1837:
1834:
1833:
1830:
1827:
1825:
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1802:
1800:
1797:
1795:
1792:
1788:
1785:
1783:
1780:
1778:
1777:
1773:
1771:
1768:
1766:
1765:
1761:
1759:
1756:
1754:
1751:
1749:
1746:
1742:
1739:
1737:
1734:
1733:
1730:
1727:
1725:
1721:
1717:
1709:
1688:
1682:
1673:
1668:
1661:
1657:
1653:
1648:
1644:
1640:
1633:
1629:
1625:
1620:
1615:
1610:
1604:
1600:
1588:
1582:
1577:
1573:
1564:
1561:
1558:
1554:
1550:
1546:
1540:
1531:
1526:
1520:
1511:
1504:
1500:
1496:
1491:
1486:
1482:
1478:
1472:
1463:
1456:
1452:
1448:
1443:
1438:
1433:
1428:
1422:
1418:
1406:
1400:
1395:
1391:
1382:
1379:
1376:
1372:
1368:
1366:
1361:
1358:
1355:
1352:
1344:
1339:
1333:
1324:
1317:
1313:
1309:
1304:
1299:
1294:
1288:
1279:
1272:
1268:
1264:
1259:
1254:
1250:
1246:
1240:
1231:
1224:
1220:
1216:
1211:
1206:
1202:
1198:
1192:
1183:
1176:
1172:
1168:
1163:
1158:
1153:
1147:
1143:
1131:
1125:
1120:
1116:
1107:
1104:
1101:
1097:
1093:
1091:
1086:
1083:
1080:
1077:
1069:
1063:
1054:
1047:
1043:
1039:
1034:
1029:
1024:
1018:
1009:
1002:
998:
994:
989:
984:
978:
974:
962:
956:
951:
947:
938:
935:
932:
928:
924:
922:
917:
914:
911:
908:
901:
898:
895:
892:
887:
884:
880:
873:
867:
862:
858:
853:
848:
844:
840:
834:
825:
821:
818:
813:
804:
797:
793:
789:
784:
779:
774:
768:
764:
752:
746:
741:
737:
728:
725:
722:
718:
714:
712:
707:
704:
701:
690:
689:
688:
672:
669:
666:
652:
650:
648:
633:
616:
598:
593:
577:
574:-dimensional
573:
569:
568:machine words
565:
560:
557:
553:
549:
545:
540:
536:
532:
528:
524:
520:
516:
510:
506:
502:
497:
494:
490:
486:
477:
470:
466:
462:
458:
454:
450:
446:
442:
436:
432:
428:
423:
421:
417:
413:
404:
397:
395:
389:
387:
380:
376:
372:
367:
363:
361:
360:Boolean state
357:
352:
350:
346:
342:
335:
331:
327:
322:
320:
316:
309:
305:
301:
296:
293:
289:
285:
277:
272:
265:
263:
257:
254:For unsigned
252:
246:
236:
232:
227:
225:
221:
217:
213:
209:
203:
195:
193:
186:
184:
182:
181:architectural
178:
172:
170:
166:
162:
158:
154:
150:
146:
139:
138:Offset binary
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
4092:
4083:
4074:
4063:. Retrieved
4053:
4045:
4037:
4028:
4004:
3993:. Retrieved
3969:. Retrieved
3959:
3948:. Retrieved
3938:
3927:. Retrieved
3903:. Retrieved
3893:
3882:. Retrieved
3877:
3868:
3857:. Retrieved
3853:
3844:
3818:. Retrieved
3808:
3778:Karnaugh map
3694:
3661:Rotate right
3649:Has inverse
3643:
3571:
3452:machine code
3445:
3347:
3219:
3216:
3213:Applications
3166:
3162:
3140:
3125:
3067:
3061:
3053:
3049:
3027:>>>
2999:
2996:>>>
2981:
2977:<<<
2973:>>>
2958:
2926:
2836:
2832:
2718:
2615:
2607:
2600:
2589:
2556:
2533:
2528:
2524:
2508:
2506:
2500:
2499:
2464:cryptography
2459:
2457:
2422:bit rotation
2421:
2417:
2413:
2411:
2392:
2387:
2385:
2327:
2319:
2317:
2312:
2302:
2297:
2290:
2285:
2276:
2274:
2190:
2175:
2171:
2169:
2061:equivalents
1775:
1763:
1740:
1735:
1728:
1713:
656:
576:vector space
571:
563:
561:
546:
543:
538:
534:
530:
526:
522:
518:
513:
508:
504:
500:
484:
482:
464:
460:
456:
452:
448:
444:
439:
437:(decimal 7)
434:
430:
426:
411:
409:
393:
383:
378:
374:
370:
364:
353:
348:
345:masking tape
340:
338:
333:
329:
325:
318:
314:
312:
310:(decimal 1)
307:
303:
299:
283:
281:
253:
242:
234:
230:
211:
207:
205:
190:
173:
148:
142:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
3901:. Microsoft
3816:. CMicrotek
3678:Shift right
3666:No inverse
3658:Rotate left
3133:to 1 or 0.
3131:units place
1724:truth table
485:bitwise XOR
347:covers, or
341:bit masking
292:logical AND
284:bitwise AND
208:bitwise NOT
110:August 2018
18:Bitwise NOT
4149:Categories
4065:2014-03-08
4029:oracle.com
3995:2015-08-11
3971:2015-08-12
3950:2015-08-11
3929:2015-08-12
3905:2013-07-14
3884:2015-09-07
3859:2016-07-06
3820:2015-08-12
3800:References
3783:Logic gate
3710:* / %
3675:Shift left
3223:pseudocode
3127:JavaScript
3122:JavaScript
2949:intrinsics
2945:Visual C++
2929:intrinsics
2523:just have
2306:carry flag
2230:ordering:
2228:Big-endian
2212:ordering:
2198:big-endian
2172:bit shifts
2166:Bit shifts
412:bitwise OR
200:See also:
179:and other
153:bit string
80:newspapers
3562:x ^ x = 0
3552:x ^ 0 = x
3530:~(~x) = x
3518:x | x = x
3508:x | 0 = x
2622:std::rotr
2618:std::rotl
2536:word size
2507:A single
2180:Registers
2124:(p XOR q)
2112:(p AND q)
1595:⌋
1583:
1570:⌊
1555:∑
1413:⌋
1401:
1388:⌊
1373:∑
1359:
1251:−
1138:⌋
1126:
1113:⌊
1098:∑
1084:
969:⌋
957:
944:⌊
929:∑
915:
899:−
893:−
868:
759:⌋
747:
734:⌊
719:∑
705:
670:≥
657:Assuming
613:over the
552:compilers
169:processor
157:bit array
3758:Bitboard
3741:See also
3201:popcount
2992:>>
2988:<<
2969:>>
2965:<<
2904:>>
2886:<<
2871:uint32_t
2850:uint32_t
2804:>>
2786:<<
2765:uint32_t
2744:uint32_t
2727:because
2699:>>
2681:<<
2666:uint32_t
2645:uint32_t
2590:assigns
2579:<<
2563:>>
2559:<<
2324:overflow
2281:sign bit
2134:(NOT p)
2077:(NOT p)
2072:(p OR q)
2059:Bitwise
1669:⌋
1649:⌊
1641:⌋
1621:⌊
1512:⌋
1492:⌊
1464:⌋
1444:⌊
1325:⌋
1305:⌊
1280:⌋
1260:⌊
1232:⌋
1212:⌊
1184:⌋
1164:⌊
1055:⌋
1035:⌊
1010:⌋
990:⌊
881:⌋
854:⌊
805:⌋
785:⌊
556:register
278:integers
256:integers
3153:" and "
3115:i == -5
2967:" and "
2935:, like
2176:shifted
2148:(NOT q)
2117:p AND q
2105:p XOR q
2093:(NOT q)
1819:Then/if
1809:If/then
1718:of two
685:
659:
319:cleared
317:(1) or
214:, is a
94:scholar
4116:XORcat
3588:Others
3427:return
3340:return
3137:Pascal
3107:0x0200
2735:, and
2729:32 - 0
2525:rotate
2428:Rotate
2275:In an
2153:p OR q
2091:p AND
566:(i.e.
386:parity
96:
89:
82:
75:
67:
3725:&
3406:shift
3361:while
3328:shift
3325:right
3313:shift
3259:while
3195:Other
3021:aByte
2916:&
2843:Clang
2386:In a
2336:floor
2330:of a
2146:p OR
2079:AND q
615:field
487:is a
414:is a
356:flags
349:masks
286:is a
276:4-bit
210:, or
159:or a
101:JSTOR
87:books
3403:left
3352:and
3310:left
3233:and
3145:and
3074:byte
3062:byte
2961:Java
2955:Java
2868:...;
2859:...,
2841:and
2762:...;
2753:...,
2663:...;
2654:...,
2628:and
2620:and
2527:and
2521:PICs
2170:The
2136:OR q
2122:NOT
2110:NOT
2098:NOT
2084:NOT
2070:NOT
1799:XNOR
1787:NAND
229:NOT
206:The
165:bits
155:, a
147:, a
73:news
3715:+ -
3705:~ -
3700:( )
3669:AND
3655:XOR
3652:NOT
3536:XOR
3524:NOT
3458:AND
3397:xor
3382:and
3280:and
3183:shl
3159:shr
3155:shr
3151:shl
3092:int
3068:int
3048:is
3015:int
2959:In
2922:));
2839:GCC
2731:is
2714:));
2636:by
2420:or
1794:AND
1782:XOR
1753:NOR
1679:mod
1574:log
1537:mod
1517:mod
1469:mod
1392:log
1356:XOR
1330:mod
1285:mod
1237:mod
1189:mod
1117:log
1060:mod
1015:mod
948:log
912:AND
859:log
831:mod
810:mod
738:log
702:NOT
471:XOR
435:111
431:011
427:101
315:set
298:010
266:AND
196:NOT
143:In
56:by
4151::
4044:.
4027:.
4016:^
3980:^
3914:^
3876:.
3852:.
3829:^
3672:OR
3492:OR
3412:by
3334:by
3319:by
3271:if
3177::=
3101:b1
3077:b1
3012:((
2951:.
2939:,
2919:31
2819:))
2810:32
2737:32
2733:32
2705:32
2466:.
2424:.
2416:,
2346:.
2313:00
2054:1
2006:0
1998:1
1950:1
1942:1
1894:0
1886:1
1838:1
1824:OR
1776:¬q
1764:¬p
1758:Xq
1726:.
1081:OR
509:11
505:01
501:10
483:A
410:A
398:OR
324:00
282:A
251:.
4137:"
4134:.
4126:"
4068:.
4048:.
4031:.
3998:.
3974:.
3953:.
3932:.
3908:.
3887:.
3862:.
3823:.
3735:|
3730:^
3430:b
3424:c
3421:←
3418:a
3415:1
3409:c
3400:a
3394:b
3391:←
3388:b
3385:a
3379:b
3376:←
3373:c
3370:0
3367:≠
3364:a
3354:b
3350:a
3343:c
3337:1
3331:b
3322:1
3316:a
3307:a
3304:+
3301:c
3298:←
3295:c
3292:0
3289:≠
3286:)
3283:1
3277:b
3274:(
3268:0
3265:≠
3262:b
3256:0
3253:←
3250:c
3243:b
3239:a
3237:(
3235:b
3231:a
3189:;
3186:2
3180:y
3174:x
3167:y
3163:x
3117:.
3110:;
3104:|
3098:=
3095:i
3089:;
3086:5
3083:-
3080:=
3054:s
3050:n
3033:.
3030:2
3024:)
3018:)
3002:.
2913:n
2910:-
2907:(
2901:x
2898:(
2895:|
2892:)
2889:n
2883:x
2880:(
2877:=
2874:y
2865:=
2862:n
2856:=
2853:x
2828:;
2825:x
2822::
2816:n
2813:-
2807:(
2801:x
2798:(
2795:|
2792:)
2789:n
2783:x
2780:(
2777:?
2774:n
2771:=
2768:y
2759:=
2756:n
2750:=
2747:x
2721:0
2711:n
2708:-
2702:(
2696:x
2693:(
2690:|
2687:)
2684:n
2678:x
2675:(
2672:=
2669:y
2660:=
2657:n
2651:=
2648:x
2638:n
2634:x
2596:y
2592:x
2585:;
2582:2
2576:y
2573:=
2570:x
2328:n
2320:n
2298:1
2291:0
2158:1
2141:p
2129:q
2100:q
2086:p
2065:0
2051:0
2048:1
2045:0
2042:1
2039:0
2036:1
2033:0
2030:1
2027:0
2024:1
2021:0
2018:1
2015:0
2012:1
2009:0
2003:0
1995:1
1992:0
1989:0
1986:1
1983:1
1980:0
1977:0
1974:1
1971:1
1968:0
1965:0
1962:1
1959:1
1956:0
1953:0
1947:0
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98:·
91:·
84:·
77:·
50:.
20:)
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