286:. In the case of even parity, for a given set of bits, the bits whose value is 1 are counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the count of 1s in a given set of bits is already even, the parity bit's value is 0. In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set to 1 making the total count of 1s in the whole set (including the parity bit) an odd number. If the count of bits with a value of 1 is odd, the count is already odd so the parity bit's value is 0. Even parity is a special case of a
330:. The transmission medium is preset, at both end points, to agree on either odd parity or even parity. For each string of bits ready to transmit (data packet) the sender calculates its parity bit, zero or one, to make it conform to the agreed parity, even or odd. The receiver of that packet first checks that the parity of the packet as a whole is in accordance with the preset agreement, then, if there was a parity error in that packet, requests a retransmission of that packet.
43:
940:,...), which is an n-ary operator that is true if and only if an odd number of arguments is true). So the same XOR concept above applies similarly to larger RAID arrays with parity, using any number of disks. In the case of a RAID 3 array of 12 drives, 11 drives participate in the XOR calculation shown above and yield a value that is then stored on the dedicated parity drive.
978:) data entry systems (which preceded magnetic-tape systems). On the systems sold by British company ICL (formerly ICT) the 1-inch-wide (25 mm) paper tape had 8 hole positions running across it, with the 8th being for parity. 7 positions were used for the data, e.g., 7-bit ASCII. The 8th position had a hole punched in it depending on the number of data holes punched.
513:
This mechanism enables the detection of single bit errors, because if one bit gets flipped due to line noise, there will be an incorrect number of ones in the received data. In the two examples above, Bob's calculated parity value matches the parity bit in its received value, indicating there are no
835:
Should any of the three drives fail, the contents of the failed drive can be reconstructed on a replacement drive by subjecting the data from the remaining drives to the same XOR operation. If Drive 2 were to fail, its data could be rebuilt using the XOR results of the contents of the two remaining
736:
When the total number of transmitted bits, including the parity bit, is even, odd parity has the advantage that both all-zeros and all-ones patterns are detected as errors. If the total number of bits is odd, only one of the patterns is detected as an error, and the choice can be made based on what
322:
In information technology parity refers to the evenness or oddness, given any set of binary digits, of the number of those bits with value one. Because parity is determined by the state of every one of the bits, this property of parity—being dependent upon all the bits and changing its value from
598:
There is a limitation to parity schemes. A parity bit is guaranteed to detect only an odd number of bit errors. If an even number of bits have errors, the parity bit records the correct number of ones even though the data is corrupt. (See also
367:
gates output what is equivalent to a check bit that creates an even parity, and XOR logic design easily scales to any number of inputs. XOR and AND structures comprise the bulk of most integrated circuitry.
392:. On a noisy transmission medium, successful transmission can therefore take a long time or even never occur. However, parity has the advantage that it uses only a single bit and requires only a number of
733:
hardware. Recovery from the error is usually done by retransmitting the data, the details of which are usually handled by software (such as the operating system I/O routines).
1065:
714:
1107:
668:
applications in which an operation can be repeated in case of difficulty, or simply detecting the error is helpful. For example, the
1041:
377:
126:
356:
bits. In this way, using one parity bit creates "redundancy" for a region from the size of one bit to the size of one disk. See
600:
338:
260:
64:
753:. If a drive in the array fails, remaining data on the other drives can be combined with the parity data (using the Boolean
710:
characters in an 8-bit byte. Other formats are possible; 8 bits of data plus a parity bit can convey all 8-bit byte values.
352:
is the number of disks in the array. When a read error occurs, each bit in the error region is recalculated from its set of
388:
any errors, as there is no way to determine the particular bit that is corrupted. The data must be discarded entirely, and
1112:
968:
107:
79:
964:
60:
1102:
1097:
960:
86:
53:
944:
750:
389:
1012:
287:
93:
713:
In serial communication contexts, parity is usually generated and checked by interface hardware (such as a
943:
Extensions and variations on the parity bit mechanism "double," "dual," or "diagonal" parity, are used in
514:
single bit errors. Consider the following example with a transmission error in the second bit using XOR:
730:
718:
696:
385:
323:
even to odd parity if any one bit changes—allows for its use in error detection and correction schemes.
316:
312:
263:. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit
75:
307:
275:
31:
1059:
997:
1047:
1037:
726:
699:
685:
665:
384:
occurred in the transmission. The parity bit is suitable only for detecting errors; it cannot
264:
722:
267:(bytes), although they can also be applied separately to an entire message string of bits.
992:
967:. This can be combined with parity computed over multiple bits sent on a single signal, a
971:. In a parallel bus, there is one longitudinal redundancy check bit per parallel signal.
100:
677:
271:
1082:
963:
in 1951. Parity in this form, applied across multiple parallel signals, is known as a
1117:
1091:
411:
656:
Bob observes even parity, as expected, thereby failing to catch the two bit errors.
975:
397:
603:.) Consider the same example as before but with an even number of corrupted bits:
1007:
791:
To calculate parity data for the two drives, an XOR is performed on their data:
689:
256:
42:
311:
can refer to the evenness or oddness of an integer, which, when written in its
291:
1051:
414:
are communicating and Alice wants to send Bob the simple 4-bit message 1001.
681:
326:
In telecommunications the parity referred to by some protocols is for error-
17:
1083:
Different methods of generating the parity bit, among other bit operations
591:
Bob reports incorrect transmission after observing unexpected odd result.
557:
Bob reports incorrect transmission after observing unexpected odd result.
703:
393:
673:
464:
Bob reports correct transmission after observing expected even result.
363:
In electronics, transcoding data with parity can be very efficient, as
692:, it can be disregarded and refetched if it is found to be corrupted.
506:
Bob reports correct transmission after observing expected odd result.
380:
incorrectly, the parity bit will be incorrect, thus indicating that a
761:
702:, a common format is 7 data bits, an even parity bit, and one or two
407:
characters, which have 7 bits, leaving the 8th bit as a parity bit.
1002:
987:
707:
404:
1034:
Principles of communication : systems, modulation, and noise
746:
669:
334:
410:
For example, the parity bit can be computed as follows. Assume
909:
The result of that XOR calculation yields Drive 2's contents.
754:
364:
252:
36:
649:
Bob reports correct transmission though actually incorrect.
344:. Parity bits are written at the rate of one parity bit per
403:
Parity bit checking is used occasionally for transmitting
333:
In computer science the parity stripe or parity disk in a
357:
376:
If an odd number of bits (including the parity bit) are
1032:
Ziemer, RodgerE.; Tranter, William H. (17 March 2014).
913:
is then stored on Drive 2, fully repairing the array.
278:. Accordingly, there are two variants of parity bits:
916:
XOR logic is also equivalent to even parity (because
717:) and, on reception, the result made available to a
676:use parity to detect transmission errors, and many
67:. Unsourced material may be challenged and removed.
974:Parity was also used on at least some paper-tape (
664:Because of its simplicity, parity is used in many
760:For example, suppose two drives in a three-drive
747:redundant array of independent/inexpensive disks
496:Bob receives: 10011 and 10110
474:Alice wants to transmit: 1001 and 1011
454:Bob receives: 10010 and 10111
432:Alice wants to transmit: 1001 and 1011
27:Bit added to a binary string for error detection
721:such as the CPU (and so too, for instance, the
315:, can be determined just by examining only its
290:(CRC), where the 1-bit CRC is generated by the
646:Bob computes overall parity: 1^1^0^1^1 = 0
625:Alice computes even parity value: 1^0^0^1 = 0
588:Bob computes overall parity: 1^0^0^1^1 = 1
571:Alice computes even parity value: 1^0^0^1 = 0
554:Bob computes overall parity: 1^1^0^1^0 = 1
536:Alice computes parity bit value: 1^0^0^1 = 0
8:
400:for an example of an error-correcting code.
757:function) to reconstruct the missing data.
358:§ Redundant Array of Independent Disks
1064:: CS1 maint: location missing publisher (
1036:(Seventh ed.). Hoboken, New Jersey.
737:the more common error is expected to be.
706:. That format accommodates all the 7-bit
127:Learn how and when to remove this message
806: XOR
628:Alice sends: 10010
605:
574:Alice sends: 10010
516:
416:
138:
30:For broader coverage of this topic, see
1024:
684:include parity protection. Because the
623:Alice wants to transmit: 1001
569:Alice wants to transmit: 1001
539:Alice adds parity bit and sends: 10010
534:Alice wants to transmit: 1001
1057:
7:
764:array contained the following data:
745:Parity data is used by RAID arrays (
582:Bob receives: 1001
65:adding citations to reliable sources
259:. Parity bits are a simple form of
477:Alice computes parity bit value:
25:
636:Bob receives: 1
547:Bob receives: 1
484:Alice adds parity bit and sends:
442:Alice adds parity bit and sends:
435:Alice computes parity bit value:
423:Successful transmission scenario
499:Bob computes overall parity:
457:Bob computes parity:
270:The parity bit ensures that the
41:
52:needs additional citations for
1108:Error detection and correction
928:XOR ... may be treated as XOR(
601:error detection and correction
1:
969:longitudinal redundancy check
836:drives, Drive 1 and Drive 3:
832:, is then stored on Drive 3.
612:Failed transmission scenario
523:Failed transmission scenario
965:transverse redundancy check
828:The resulting parity data,
688:data is just a copy of the
1134:
961:magnetic-tape data storage
390:retransmitted from scratch
29:
959:was present on the first
565:Error in the parity bit
530:Error in the second bit
148:
145:
141:
725:) via a status bit in a
632:...TRANSMISSION ERROR...
609:Type of bit parity error
578:...TRANSMISSION ERROR...
543:...TRANSMISSION ERROR...
520:Type of bit parity error
481:1+0+1+1 (+ 1 mod 2) = 0
479:1+0+0+1 (+ 1 mod 2) = 1
149:8 bits including parity
288:cyclic redundancy check
903:Reconstructed Drive 2
503:1+0+1+1+0 (mod 2) = 1
501:1+0+0+1+1 (mod 2) = 1
461:1+0+1+1+1 (mod 2) = 0
459:1+0+0+1+0 (mod 2) = 0
272:total number of 1-bits
317:least significant bit
255:added to a string of
1113:Parity (mathematics)
619:Two corrupted bits
439:1+0+1+1 (mod 2) = 1
437:1+0+0+1 (mod 2) = 0
261:error detecting code
61:improve this article
32:Parity (mathematics)
1013:Thue–Morse sequence
998:Single-event upset
420:Type of bit parity
146:(count of 1-bits)
1103:Data transmission
1098:Binary arithmetic
907:
906:
861:
860:
826:
825:
789:
788:
727:hardware register
700:data transmission
686:Instruction cache
654:
653:
596:
595:
511:
510:
396:to generate. See
274:in the string is
241:
240:
137:
136:
129:
111:
16:(Redirected from
1125:
1070:
1069:
1063:
1055:
1029:
866:
865:
839:
838:
794:
793:
767:
766:
723:operating system
606:
517:
417:
139:
132:
125:
121:
118:
112:
110:
69:
45:
37:
21:
1133:
1132:
1128:
1127:
1126:
1124:
1123:
1122:
1088:
1087:
1079:
1074:
1073:
1056:
1044:
1031:
1030:
1026:
1021:
993:Parity function
984:
953:
888:
813:
743:
662:
502:
500:
485:
480:
478:
460:
458:
443:
438:
436:
374:
372:Error detection
305:In mathematics
303:
280:even parity bit
143:
133:
122:
116:
113:
70:
68:
58:
46:
35:
28:
23:
22:
15:
12:
11:
5:
1131:
1129:
1121:
1120:
1115:
1110:
1105:
1100:
1090:
1089:
1086:
1085:
1078:
1077:External links
1075:
1072:
1071:
1042:
1023:
1022:
1020:
1017:
1016:
1015:
1010:
1005:
1000:
995:
990:
983:
980:
952:
949:
905:
904:
901:
896:
893:
892:
889:
884:
882:
878:
877:
874:
869:
859:
858:
853:
849:
848:
843:
824:
823:
818:
815:
814:
809:
807:
803:
802:
797:
787:
786:
781:
777:
776:
771:
742:
739:
678:microprocessor
661:
658:
652:
651:
621:
614:
613:
610:
594:
593:
567:
560:
559:
532:
525:
524:
521:
509:
508:
471:
467:
466:
429:
425:
424:
421:
373:
370:
302:
299:
284:odd parity bit
239:
238:
232:
226:
223:
219:
218:
212:
206:
203:
199:
198:
192:
186:
183:
179:
178:
172:
166:
163:
159:
158:
155:
151:
150:
147:
144:
142:7 bits of data
135:
134:
49:
47:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1130:
1119:
1116:
1114:
1111:
1109:
1106:
1104:
1101:
1099:
1096:
1095:
1093:
1084:
1081:
1080:
1076:
1067:
1061:
1053:
1049:
1045:
1043:9781118078914
1039:
1035:
1028:
1025:
1018:
1014:
1011:
1009:
1006:
1004:
1001:
999:
996:
994:
991:
989:
986:
985:
981:
979:
977:
972:
970:
966:
962:
958:
950:
948:
946:
941:
939:
935:
931:
927:
923:
919:
914:
912:
902:
900:
897:
895:
894:
890:
887:
883:
880:
879:
875:
873:
870:
868:
867:
864:
857:
854:
851:
850:
847:
844:
841:
840:
837:
833:
831:
822:
819:
817:
816:
812:
808:
805:
804:
801:
798:
796:
795:
792:
785:
782:
779:
778:
775:
772:
769:
768:
765:
763:
758:
756:
752:
749:) to achieve
748:
740:
738:
734:
732:
728:
724:
720:
716:
711:
709:
705:
701:
698:
693:
691:
687:
683:
679:
675:
671:
667:
659:
657:
650:
647:
644:
643:
639:
634:
633:
629:
626:
622:
620:
616:
615:
611:
608:
607:
604:
602:
592:
589:
586:
585:
580:
579:
575:
572:
568:
566:
562:
561:
558:
555:
552:
550:
545:
544:
540:
537:
533:
531:
527:
526:
522:
519:
518:
515:
507:
504:
497:
494:
493:
489:
482:
475:
472:
469:
468:
465:
462:
455:
452:
451:
447:
440:
433:
430:
427:
426:
422:
419:
418:
415:
413:
412:Alice and Bob
408:
406:
401:
399:
395:
391:
387:
383:
379:
371:
369:
366:
361:
359:
355:
351:
347:
343:
342:
336:
331:
329:
324:
320:
318:
314:
310:
309:
300:
298:
296:
293:
289:
285:
281:
277:
273:
268:
266:
262:
258:
254:
250:
246:
237:
233:
231:
227:
224:
221:
220:
217:
213:
211:
207:
204:
201:
200:
197:
193:
191:
187:
184:
181:
180:
177:
173:
171:
167:
164:
161:
160:
156:
153:
152:
140:
131:
128:
120:
109:
106:
102:
99:
95:
92:
88:
85:
81:
78: –
77:
73:
72:Find sources:
66:
62:
56:
55:
50:This article
48:
44:
39:
38:
33:
19:
1033:
1027:
976:punched tape
973:
957:parity track
956:
954:
942:
937:
933:
929:
925:
921:
917:
915:
910:
908:
898:
885:
871:
863:as follows:
862:
855:
845:
834:
829:
827:
820:
810:
799:
790:
783:
773:
759:
744:
735:
712:
694:
680:instruction
663:
655:
648:
645:
641:
637:
635:
631:
630:
627:
624:
618:
617:Even parity
597:
590:
587:
583:
581:
577:
576:
573:
570:
564:
563:Even parity
556:
553:
548:
546:
542:
541:
538:
535:
529:
528:Even parity
512:
505:
498:
495:
491:
487:
483:
476:
473:
463:
456:
453:
449:
445:
441:
434:
431:
409:
402:
398:Hamming code
382:parity error
381:
375:
362:
353:
349:
348:bits, where
345:
340:
332:
327:
325:
321:
306:
304:
294:
283:
279:
269:
248:
244:
242:
235:
229:
215:
209:
195:
189:
175:
169:
123:
117:January 2022
114:
104:
97:
90:
83:
76:"Parity bit"
71:
59:Please help
54:verification
51:
1008:Check digit
690:main memory
428:Even parity
378:transmitted
313:binary form
276:even or odd
257:binary code
18:Even parity
1092:Categories
1019:References
751:redundancy
741:RAID array
470:Odd parity
341:correction
292:polynomial
245:parity bit
87:newspapers
1060:cite book
1052:856647730
852:Drive 3:
842:Drive 1:
780:Drive 2:
770:Drive 1:
731:interface
719:processor
704:stop bits
674:PCI buses
394:XOR gates
337:provides
328:detection
249:check bit
982:See also
911:11010100
899:11010100
891:Drive 3
886:10111001
876:Drive 1
872:01101101
856:10111001
846:01101101
830:10111001
821:10111001
811:11010100
800:01101101
784:11010100
774:01101101
666:hardware
490:and 1011
448:and 1011
222:1111111
202:1101001
182:1010001
162:0000000
951:History
945:RAID-DP
729:in the
386:correct
360:below.
251:, is a
234:1111111
228:1111111
214:1101001
208:1101001
194:1010001
188:1010001
174:0000000
168:0000000
101:scholar
1050:
1040:
762:RAID 4
697:serial
682:caches
339:error-
308:parity
301:Parity
265:octets
103:
96:
89:
82:
74:
1003:8-N-1
988:BIP-8
708:ASCII
660:Usage
405:ASCII
247:, or
154:even
108:JSTOR
94:books
1118:RAID
1066:link
1048:OCLC
1038:ISBN
924:XOR
920:XOR
715:UART
672:and
670:SCSI
551:010
486:1001
444:1001
335:RAID
297:+1.
282:and
157:odd
80:news
881:XOR
755:XOR
695:In
365:XOR
319:.
253:bit
63:by
1094::
1062:}}
1058:{{
1046:.
955:A
947:.
640:01
243:A
225:7
205:4
185:3
165:0
1068:)
1054:.
938:c
936:,
934:b
932:,
930:a
926:c
922:b
918:a
642:1
638:1
584:1
549:1
492:0
488:1
450:1
446:0
354:n
350:n
346:n
295:x
236:0
230:1
216:1
210:0
196:0
190:1
176:1
170:0
130:)
124:(
119:)
115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
