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BinaryNumbersSummary
Therearedifferentnumberingsystemsusedindigitalelectroniccircuitsandcomputers.However,thenumbering
systemusedinonetypeofcircuitmaybedifferenttothatofanothertypeofcircuit,forexample,thememoryofacomputer
wouldusehexadecimalnumberswhilethekeyboardusesdecimalnumbers.Thentheconversionfromonenumber
systemtoanotherisveryimportantwiththefourmainformsofarithmeticbeing.
Decimal-Thedecimalnumberingsystemhasabaseof10(MOD-10)andusesthedigits
from0through9torepresentadecimalnumbervalue.
Binary-Thebinarynumberingsystemhasabaseof2(MOD-2)andusesonlytwodigitsa"0"
anda"1"torepresentabinarynumbervalue.
Octal-Theoctalnumberingsystemhasabaseof8(MOD-8)anduses8digits
between0and7torepresentanoctalnumbervalue.
Hexadecimal-TheHexadecimalnumberingsystemhasabaseof16(MOD-16)andusesa
totalof16numericandalphabeticcharacterstorepresentanumbervalue.Hexadecimal
numbersconsistofdigits0through9andlettersAtoF.
Longbinarynumbersaredifficulttobothreadorwriteandaregenerallyconvertedintoasystemmoreeasilyunderstood
oruserfriendly.ThetwomostcommonderivativesbasedonbinarynumbersaretheOctaland
theHexadecimalnumberingsystems,withbothoftheselimitedinlengthtoabyte(8-bits)oraword(16-bits).
Octalnumberscanberepresentedbygroupsof3-bitsandhexadecimalnumbersbygroupsof4-bitstogether,withthis
groupingofthebitsbeingusedinelectronicorcomputersystemsindisplaysorprintouts.Thegroupingtogetherof
binarynumberscanalsobeusedtorepresentMachineCodeusedforprogramminginstructionsandcontrolsuchas
anAssemblyLanguage.
ComparisonsbetweenthevariousDecimal,Binary,HexadecimalandOctalnumbersaregiveninthefollowingtable.
ComparisonTable
Base,bByte(8-bits)Word(16-bits)
Decimal
0
to
255
0
to
65,535
Binary
00000000
to
11111111
0000000000000000
to
1111111111111111
Hexadecimal
00
to
FF
0000
to
FFFF
Octal
000
to
377
000000
to
177777
WecanseefromthetableabovethattheHexadecimalnumberingsystemusesonlyfourdigitstoexpressasingle16-bit
1010
22
1616
88
wordlength,andasaresultitisthemostcommonlyusedBaseNumberingSystemfordigital,micro-electronicand
computersystems.
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