169:
44:
56:
487:
355:
164:, sensitive messages may be concealed by manipulating and storing information in the least significant bits of an image or a sound file. The user may later recover this information by extracting the least significant bits of the manipulated pixels to recover the original message. This allows the storage or transfer of digital information to remain concealed.
186:
This table illustrates an example of decimal value of 149 and the location of LSb. In this particular example, the position of unit value (decimal 1 or 0) is located in bit position 0 (n = 0). MSb stands for
589:
820:
458:
174:
A diagram showing how manipulating the least significant bits of a color can have a very subtle and generally unnoticeable affect on the color. In this diagram, green is represented by its
129:
Bit indexing correlates to the positional notation of the value in base 2. For this reason, bit index is not affected by how the value is stored on the device, such as the value's
667:
714:
687:
626:
740:
178:
value, both in decimal and in binary. The red box surrounding the last two bits illustrates the least significant bits changed in the binary representation.
515:
758:
396:
929:
861:
133:. Rather, it is a property of the numeric value in binary itself. This is often utilized in programming via
976:
379:
971:
387:
87:
631:
98:) represents the highest-order place of the binary integer. The LSb is sometimes referred to as the
110:
of writing less significant digits further to the right. The MSb is similarly referred to as the
134:
892:
881:
302:
are indications on the ordering of the sequence of the bits in the bytes sent over a wire in a
856:
367:
359:
331:
84:
60:
48:
32:
921:
914:
699:
672:
499:
491:
63:
representation of decimal 149, with the MSb highlighted. The MSb represents a value of 128.
602:
8:
866:
312:
means that the most significant bit will arrive first: hence e.g. the hexadecimal number
303:
107:
945:
725:
925:
717:
690:
876:
168:
375:
119:
887:
965:
161:
118:. In both cases, the LSb and MSb correlate directly to the least significant
51:
of decimal 149, with the LSb highlighted. The LSb represents a value of 1.
43:
871:
130:
55:
851:
68:
20:
836:
342:
in binary representation, will arrive as the (reversed) sequence
155:
123:
752:
For MSb 1 numbering, the value of an unsigned binary integer is
490:
MSb 0: A container for 8-bit binary number with the highlighted
358:
LSb 0: A container for 8-bit binary number with the highlighted
90:
representing the binary 1s place of the integer. Similarly, the
383:
825:
374:. This bit numbering method has the advantage that for any
599:
LSb of a number can be calculated with time complexity of
334:
will arrive first: hence e.g. the same hexadecimal number
175:
80:
28:
486:
354:
289:
320:
in binary representation, will arrive as the sequence
761:
728:
702:
675:
634:
605:
584:{\displaystyle \sum _{i=0}^{N-1}b_{i}\cdot 2^{N-1-i}}
518:
509:
The value of an unsigned binary integer is therefore
399:
378:the value of the number can be calculated by using
913:
814:
734:
708:
681:
661:
620:
583:
452:
815:{\displaystyle \sum _{i=1}^{N}b_{i}\cdot 2^{N-i}}
453:{\displaystyle \sum _{i=0}^{N-1}b_{i}\cdot 2^{i}}
963:
911:
306:protocol or in a stream (e.g. an audio stream).
38:
832:strings starting with 1 for the leftmost bit.
498:When the bit numbering starts at zero for the
366:When the bit numbering starts at zero for the
156:Least significant bit in digital steganography
386:of 2. The value of an unsigned binary
181:
232:Bit weight for given bit position n ( 2 )
470:denotes the value of the bit with number
148:bit of a binary integer (with a value of
485:
353:
54:
42:
27:is the convention used to identify the
964:
481:
349:
502:(MSb) the numbering scheme is called
478:denotes the number of bits in total.
370:(LSb) the numbering scheme is called
842:function uses LSb 0 numbering.
290:Most- vs least-significant bit first
16:Convention to identify bit positions
13:
893:MAC address: Bit-reversed notation
676:
638:
594:
14:
988:
920:. Computeach Press Inc. p.
662:{\displaystyle a\And (\sim a+1)}
167:
122:and most significant digit of a
938:
905:
656:
641:
615:
609:
1:
898:
862:Signed number representations
300:least significant bit at last
39:Bit significance and indexing
7:
845:
328:Least significant bit first
106:, due to the convention in
10:
993:
382:with the bit number and a
310:Most significant bit first
296:most significant bit first
912:Langdon, Glen G. (1982).
494:assigned the bit number 0
362:assigned the bit number 0
747:
182:Unsigned integer example
191:, while LSb stands for
882:Unit in the last place
816:
782:
736:
710:
683:
663:
622:
585:
545:
495:
454:
426:
363:
201:Binary (Decimal: 149)
64:
52:
857:Binary numeral system
817:
762:
737:
711:
709:{\displaystyle \sim }
684:
682:{\displaystyle \And }
664:
623:
586:
519:
489:
455:
400:
368:least significant bit
360:least significant bit
357:
332:least significant bit
193:least significant bit
73:least significant bit
58:
49:binary representation
46:
759:
726:
700:
673:
632:
621:{\displaystyle O(n)}
603:
516:
500:most significant bit
492:most significant bit
397:
189:most significant bit
92:most significant bit
482:MSb 0 bit numbering
350:LSb 0 bit numbering
304:serial transmission
263:Bit position label
144:corresponds to the
108:positional notation
977:Assembly languages
812:
732:
706:
679:
659:
618:
581:
496:
450:
364:
65:
53:
972:Binary arithmetic
735:{\displaystyle a}
718:bitwise operation
691:bitwise operation
287:
286:
984:
956:
955:
953:
952:
942:
936:
935:
919:
909:
877:Binary logarithm
867:Two's complement
821:
819:
818:
813:
811:
810:
792:
791:
781:
776:
741:
739:
738:
733:
715:
713:
712:
707:
688:
686:
685:
680:
668:
666:
665:
660:
627:
625:
624:
619:
590:
588:
587:
582:
580:
579:
555:
554:
544:
533:
459:
457:
456:
451:
449:
448:
436:
435:
425:
414:
345:
341:
337:
323:
319:
315:
294:The expressions
198:
197:
171:
151:
143:
992:
991:
987:
986:
985:
983:
982:
981:
962:
961:
960:
959:
950:
948:
944:
943:
939:
932:
916:Computer Design
910:
906:
901:
848:
841:
831:
800:
796:
787:
783:
777:
766:
760:
757:
756:
750:
727:
724:
723:
701:
698:
697:
674:
671:
670:
633:
630:
629:
604:
601:
600:
597:
595:LSb calculation
563:
559:
550:
546:
534:
523:
517:
514:
513:
484:
468:
444:
440:
431:
427:
415:
404:
398:
395:
394:
376:unsigned number
352:
344:0 1 0 0 1 0 0 0
343:
339:
335:
330:means that the
322:0 0 0 1 0 0 1 0
321:
317:
313:
292:
184:
158:
149:
138:
41:
31:positions in a
17:
12:
11:
5:
990:
980:
979:
974:
958:
957:
937:
930:
903:
902:
900:
897:
896:
895:
890:
888:Find first set
885:
879:
874:
869:
864:
859:
854:
847:
844:
839:
829:
823:
822:
809:
806:
803:
799:
795:
790:
786:
780:
775:
772:
769:
765:
749:
746:
731:
705:
678:
658:
655:
652:
649:
646:
643:
640:
637:
617:
614:
611:
608:
596:
593:
592:
591:
578:
575:
572:
569:
566:
562:
558:
553:
549:
543:
540:
537:
532:
529:
526:
522:
483:
480:
466:
461:
460:
447:
443:
439:
434:
430:
424:
421:
418:
413:
410:
407:
403:
380:exponentiation
351:
348:
291:
288:
285:
284:
279:
277:
275:
273:
271:
269:
267:
264:
260:
259:
254:
251:
248:
245:
242:
239:
236:
233:
229:
228:
223:
220:
217:
214:
211:
208:
205:
202:
183:
180:
157:
154:
112:high-order bit
104:right-most bit
83:position in a
40:
37:
15:
9:
6:
4:
3:
2:
989:
978:
975:
973:
970:
969:
967:
947:
946:"Bit Numbers"
941:
933:
931:0-9607864-0-6
927:
923:
918:
917:
908:
904:
894:
891:
889:
886:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
849:
843:
838:
833:
827:
807:
804:
801:
797:
793:
788:
784:
778:
773:
770:
767:
763:
755:
754:
753:
745:
744:
729:
722:
719:
703:
695:
692:
653:
650:
647:
644:
635:
628:with formula
612:
606:
576:
573:
570:
567:
564:
560:
556:
551:
547:
541:
538:
535:
530:
527:
524:
520:
512:
511:
510:
507:
505:
501:
493:
488:
479:
477:
473:
469:
445:
441:
437:
432:
428:
422:
419:
416:
411:
408:
405:
401:
393:
392:
391:
390:is therefore
389:
385:
381:
377:
373:
369:
361:
356:
347:
333:
329:
325:
311:
307:
305:
301:
297:
283:
280:
278:
276:
274:
272:
270:
268:
265:
262:
261:
258:
255:
252:
249:
246:
243:
240:
237:
234:
231:
230:
227:
224:
221:
218:
215:
212:
209:
206:
203:
200:
199:
196:
194:
190:
179:
177:
172:
170:
165:
163:
162:steganography
153:
147:
142:
137:: A value of
136:
132:
127:
125:
121:
117:
116:left-most bit
113:
109:
105:
101:
100:low-order bit
97:
93:
89:
86:
82:
78:
74:
70:
62:
59:The unsigned
57:
50:
45:
36:
34:
33:binary number
30:
26:
25:bit numbering
22:
949:. Retrieved
940:
915:
907:
834:
824:
751:
742:
720:
693:
598:
508:
503:
497:
475:
471:
464:
462:
371:
365:
327:
326:
309:
308:
299:
295:
293:
281:
256:
225:
192:
188:
185:
173:
166:
159:
145:
140:
135:bit shifting
128:
115:
111:
103:
99:
95:
91:
76:
72:
66:
24:
18:
160:In digital
139:1 <<
966:Categories
951:2021-03-30
899:References
872:Endianness
504:MSb 0
372:LSb 0
131:byte order
852:ARINC 429
805:−
794:⋅
764:∑
704:∼
677:&
645:∼
639:&
574:−
568:−
557:⋅
539:−
521:∑
438:⋅
420:−
402:∑
126:integer.
79:) is the
69:computing
21:computing
846:See also
828:numbers
669:, where
340:00010010
338:, again
318:00010010
837:Fortran
388:integer
124:decimal
88:integer
928:
721:NOT on
716:means
689:means
474:, and
463:where
85:binary
71:, the
61:binary
884:(ULP)
840:BTEST
748:Other
120:digit
926:ISBN
835:The
826:PL/I
696:and
384:base
336:0x12
314:0x12
298:and
266:MSb
47:The
830:BIT
694:AND
282:LSb
195:.
176:RGB
152:).
114:or
102:or
96:MSb
81:bit
77:LSb
67:In
29:bit
19:In
968::
924:.
922:52
506:.
346:.
324:.
316:,
253:2
250:2
247:2
244:2
241:2
238:2
235:2
222:0
219:1
216:0
213:1
210:0
207:0
204:1
35:.
23:,
954:.
934:.
808:i
802:N
798:2
789:i
785:b
779:N
774:1
771:=
768:i
743:.
730:a
657:)
654:1
651:+
648:a
642:(
636:a
616:)
613:n
610:(
607:O
577:i
571:1
565:N
561:2
552:i
548:b
542:1
536:N
531:0
528:=
525:i
476:N
472:i
467:i
465:b
446:i
442:2
433:i
429:b
423:1
417:N
412:0
409:=
406:i
257:2
226:1
150:2
146:n
141:n
94:(
75:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
