180:
55:
67:
175:, 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.
498:
366:
197:
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
600:
831:
469:
185:
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
140:
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
678:
725:
698:
637:
751:
189:
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.
940:
526:
872:
769:
407:
987:
982:
398:
98:
144:. Rather, it is a property of the numeric value in binary itself. This is often utilized in programming via
892:
867:
378:
370:
342:
95:
71:
59:
43:
642:
510:
502:
179:
109:) represents the highest-order place of the binary integer. The LSb is sometimes referred to as the
877:
390:
314:
118:
121:
of writing less significant digits further to the right. The MSb is similarly referred to as the
313:
are indications on the ordering of the sequence of the bits in the bytes sent over a wire in a
936:
728:
701:
145:
887:
932:
925:
710:
683:
74:
representation of decimal 149, with the MSb highlighted. The MSb represents a value of 128.
613:
386:
130:
323:
means that the most significant bit will arrive first: hence e.g. the hexadecimal number
956:
898:
736:
54:
976:
172:
66:
903:
17:
882:
141:
129:. In both cases, the LSb and MSb correlate directly to the least significant
862:
79:
31:
62:
of decimal 149, with the LSb highlighted. The LSb represents a value of 1.
847:
134:
496:
394:
364:
65:
53:
353:
in binary representation, will arrive as the (reversed) sequence
836:
763:
For MSb 1 numbering, the value of an unsigned binary integer is
501:
MSb 0: A container for 8-bit binary number with the highlighted
369:
LSb 0: A container for 8-bit binary number with the highlighted
101:
representing the binary 1s place of the integer. Similarly, the
497:
365:
186:
91:
39:
385:. This bit numbering method has the advantage that for any
610:
LSb of a number can be calculated with time complexity of
345:
will arrive first: hence e.g. the same hexadecimal number
331:
in binary representation, will arrive as the sequence
772:
739:
713:
686:
645:
616:
595:{\displaystyle \sum _{i=0}^{N-1}b_{i}\cdot 2^{N-1-i}}
529:
520:
The value of an unsigned binary integer is therefore
410:
389:the value of the number can be calculated by using
924:
825:
745:
719:
692:
672:
631:
594:
463:
826:{\displaystyle \sum _{i=1}^{N}b_{i}\cdot 2^{N-i}}
464:{\displaystyle \sum _{i=0}^{N-1}b_{i}\cdot 2^{i}}
317:protocol or in a stream (e.g. an audio stream).
843:strings starting with 1 for the leftmost bit.
509:When the bit numbering starts at zero for the
377:When the bit numbering starts at zero for the
167:Least significant bit in digital steganography
8:
397:of 2. The value of an unsigned binary
243:Bit weight for given bit position n ( 2 )
811:
798:
788:
777:
771:
738:
712:
685:
644:
615:
574:
561:
545:
534:
528:
481:denotes the value of the bit with number
455:
442:
426:
415:
409:
159:bit of a binary integer (with a value of
208:
915:
38:is the convention used to identify the
513:(MSb) the numbering scheme is called
489:denotes the number of bits in total.
381:(LSb) the numbering scheme is called
7:
853:function uses LSb 0 numbering.
301:Most- vs least-significant bit first
27:Convention to identify bit positions
904:MAC address: Bit-reversed notation
687:
649:
25:
931:. Computeach Press Inc. p.
673:{\displaystyle a\And (\sim a+1)}
178:
133:and most significant digit of a
667:
652:
626:
620:
1:
873:Signed number representations
311:least significant bit at last
50:Bit significance and indexing
339:Least significant bit first
117:, due to the convention in
1004:
393:with the bit number and a
321:Most significant bit first
307:most significant bit first
923:Langdon, Glen G. (1982).
505:assigned the bit number 0
373:assigned the bit number 0
193:Unsigned integer example
202:, while LSb stands for
893:Unit in the last place
827:
793:
747:
721:
694:
674:
633:
596:
556:
506:
465:
437:
374:
212:Binary (Decimal: 149)
75:
63:
868:Binary numeral system
828:
773:
748:
722:
720:{\displaystyle \sim }
695:
693:{\displaystyle \And }
675:
634:
597:
530:
500:
466:
411:
379:least significant bit
371:least significant bit
368:
343:least significant bit
204:least significant bit
84:least significant bit
69:
60:binary representation
57:
770:
737:
711:
684:
643:
632:{\displaystyle O(n)}
614:
527:
511:most significant bit
503:most significant bit
408:
200:most significant bit
103:most significant bit
493:MSb 0 bit numbering
361:LSb 0 bit numbering
315:serial transmission
274:Bit position label
155:corresponds to the
119:positional notation
988:Assembly languages
823:
743:
717:
690:
670:
629:
592:
507:
461:
375:
76:
64:
983:Binary arithmetic
746:{\displaystyle a}
729:bitwise operation
702:bitwise operation
298:
297:
16:(Redirected from
995:
967:
966:
964:
963:
953:
947:
946:
930:
920:
888:Binary logarithm
878:Two's complement
832:
830:
829:
824:
822:
821:
803:
802:
792:
787:
752:
750:
749:
744:
726:
724:
723:
718:
699:
697:
696:
691:
679:
677:
676:
671:
638:
636:
635:
630:
601:
599:
598:
593:
591:
590:
566:
565:
555:
544:
470:
468:
467:
462:
460:
459:
447:
446:
436:
425:
356:
352:
348:
334:
330:
326:
305:The expressions
209:
182:
162:
154:
21:
1003:
1002:
998:
997:
996:
994:
993:
992:
973:
972:
971:
970:
961:
959:
955:
954:
950:
943:
927:Computer Design
922:
921:
917:
912:
859:
852:
842:
807:
794:
768:
767:
761:
735:
734:
709:
708:
682:
681:
641:
640:
612:
611:
608:
606:LSb calculation
570:
557:
525:
524:
495:
479:
451:
438:
406:
405:
387:unsigned number
363:
355:0 1 0 0 1 0 0 0
354:
350:
346:
341:means that the
333:0 0 0 1 0 0 1 0
332:
328:
324:
303:
195:
169:
160:
149:
52:
42:positions in a
28:
23:
22:
18:Significant bit
15:
12:
11:
5:
1001:
999:
991:
990:
985:
975:
974:
969:
968:
948:
941:
914:
913:
911:
908:
907:
906:
901:
899:Find first set
896:
890:
885:
880:
875:
870:
865:
858:
855:
850:
840:
834:
833:
820:
817:
814:
810:
806:
801:
797:
791:
786:
783:
780:
776:
760:
757:
742:
716:
689:
669:
666:
663:
660:
657:
654:
651:
648:
628:
625:
622:
619:
607:
604:
603:
602:
589:
586:
583:
580:
577:
573:
569:
564:
560:
554:
551:
548:
543:
540:
537:
533:
494:
491:
477:
472:
471:
458:
454:
450:
445:
441:
435:
432:
429:
424:
421:
418:
414:
391:exponentiation
362:
359:
302:
299:
296:
295:
290:
288:
286:
284:
282:
280:
278:
275:
271:
270:
265:
262:
259:
256:
253:
250:
247:
244:
240:
239:
234:
231:
228:
225:
222:
219:
216:
213:
194:
191:
168:
165:
123:high-order bit
115:right-most bit
94:position in a
51:
48:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1000:
989:
986:
984:
981:
980:
978:
958:
957:"Bit Numbers"
952:
949:
944:
942:0-9607864-0-6
938:
934:
929:
928:
919:
916:
909:
905:
902:
900:
897:
894:
891:
889:
886:
884:
881:
879:
876:
874:
871:
869:
866:
864:
861:
860:
856:
854:
849:
844:
838:
818:
815:
812:
808:
804:
799:
795:
789:
784:
781:
778:
774:
766:
765:
764:
758:
756:
755:
740:
733:
730:
714:
706:
703:
664:
661:
658:
655:
646:
639:with formula
623:
617:
605:
587:
584:
581:
578:
575:
571:
567:
562:
558:
552:
549:
546:
541:
538:
535:
531:
523:
522:
521:
518:
516:
512:
504:
499:
492:
490:
488:
484:
480:
456:
452:
448:
443:
439:
433:
430:
427:
422:
419:
416:
412:
404:
403:
402:
401:is therefore
400:
396:
392:
388:
384:
380:
372:
367:
360:
358:
344:
340:
336:
322:
318:
316:
312:
308:
300:
294:
291:
289:
287:
285:
283:
281:
279:
276:
273:
272:
269:
266:
263:
260:
257:
254:
251:
248:
245:
242:
241:
238:
235:
232:
229:
226:
223:
220:
217:
214:
211:
210:
207:
205:
201:
192:
190:
188:
183:
181:
176:
174:
173:steganography
166:
164:
158:
153:
148:: A value of
147:
143:
138:
136:
132:
128:
127:left-most bit
124:
120:
116:
112:
111:low-order bit
108:
104:
100:
97:
93:
89:
85:
81:
73:
70:The unsigned
68:
61:
56:
49:
47:
45:
44:binary number
41:
37:
36:bit numbering
33:
19:
960:. Retrieved
951:
926:
918:
845:
835:
762:
753:
731:
704:
609:
519:
514:
508:
486:
482:
475:
473:
382:
376:
338:
337:
320:
319:
310:
306:
304:
292:
267:
236:
203:
199:
196:
184:
177:
170:
156:
151:
146:bit shifting
139:
126:
122:
114:
110:
106:
102:
87:
83:
77:
35:
29:
171:In digital
150:1 <<
977:Categories
962:2021-03-30
910:References
883:Endianness
515:MSb 0
383:LSb 0
142:byte order
863:ARINC 429
816:−
805:⋅
775:∑
715:∼
688:&
656:∼
650:&
585:−
579:−
568:⋅
550:−
532:∑
449:⋅
431:−
413:∑
137:integer.
90:) is the
80:computing
32:computing
857:See also
839:numbers
680:, where
351:00010010
349:, again
329:00010010
848:Fortran
399:integer
135:decimal
99:integer
939:
732:NOT on
727:means
700:means
485:, and
474:where
96:binary
82:, the
72:binary
895:(ULP)
851:BTEST
759:Other
131:digit
937:ISBN
846:The
837:PL/I
707:and
395:base
347:0x12
325:0x12
309:and
277:MSb
58:The
841:BIT
705:AND
293:LSb
206:.
187:RGB
163:).
125:or
113:or
107:MSb
92:bit
88:LSb
78:In
40:bit
30:In
979::
935:.
933:52
517:.
357:.
335:.
327:,
264:2
261:2
258:2
255:2
252:2
249:2
246:2
233:0
230:1
227:0
224:1
221:0
218:0
215:1
46:.
34:,
965:.
945:.
819:i
813:N
809:2
800:i
796:b
790:N
785:1
782:=
779:i
754:.
741:a
668:)
665:1
662:+
659:a
653:(
647:a
627:)
624:n
621:(
618:O
588:i
582:1
576:N
572:2
563:i
559:b
553:1
547:N
542:0
539:=
536:i
487:N
483:i
478:i
476:b
457:i
453:2
444:i
440:b
434:1
428:N
423:0
420:=
417:i
268:2
237:1
161:2
157:n
152:n
105:(
86:(
20:)
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