Page 263 - FUNDAMENTALS OF COMPUTER

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NPP Number System, Boolean Algebra and Logic Circuits 263

Arithmetic in Number System Zå~a {gñQ>‘ ‘| A§H$J{UV

The computer circuit performs various My±{H$ H$åß`yQ>a Ho$ n[anW _| gmar {H«$`mE± ~mBZar
arithmetic operations on Binary Numbers. g§»`mAm| na hmoVr h¡Ÿ Bgr{bE h_ ~mBZar Omo‹S>, KQ>md,
Therefore we will discuss Binary addition, sub- ^mJ VWm JwUm na Ü`mZ H|${ÐV H$a|JoŸ&
traction, multiplication and division.
3.28 Binary Addition 3.28 ~mBZar `moJ
There are only two Binary Digits called My±{H$ Xmo hr ~mBZar A§H$ ({~Q>) hmoVo h¢ Bg{bE BÝh|
bits which can be added in four ways. First Mma VarHo$ go Omo‹S> gH$Vo h¡Ÿ& nhbo VrZ `moJ, Vmo EH$X_
three additions look exactly similar to decimal Xe_bd `moJ Ho$ g_mZ h¢Ÿ:
addition as shown below:
0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1
But what about 1 + 1 ? Since there is no 2 bo{H$Z 1 + 1 = ? My±{H$ 2 H$m H$moB© g§Ho$V ~mBZar
like symbol in Binary, We can write its Binary _| Zhr hmoVm, Bg{bE 2 H$mo ~mBZar _| 10 {bIVo h¢Ÿ&
Equivalent which is 10. Therefore it is very
important to memorise that:
1 + 1 = 10

Now, suppose we want to add two Binary A~ `{X h_| Xmo ~mBZar g§»`mAm| H$mo Omo‹S>Zm hmo Vmo
numbers, the procedure will be exactly similar dhr {gÕm§V H$m Cn`moJ H$a|Jo Omo Xe_bd _| H$aVo h¡Ÿ&
to Decimal addition. We add the pair of bits
column–by–column. If a carry is generated it is Xmo-Xmo {~Q>m| Ho$ g_yh H$mo Omo‹S>|JoŸ& `{X hm{gc AmVm h¡
added to the next pair of bits. Now take an Vmo Cgo AJco g_yh _| Omo‹S>|Jo…
example :
1 0 1 + 0 0 1 = ?
Now start from right side, we have both 1. A~ grYo hmW go ewê$ hmoH$a 1 d 1 H$mo Omo‹S>mo Ÿ&
Thus, 1 + 1= 10. Write ‘0’ below and take carry AV: 1 + 1 = 10, ZrMo eyÝ` {bImo VWm hm{gb H$m
for the next column : 1 bmoŸ&

Carry → 1 hm{gc
1 0 1
+ 0 0 1
0
Now, perform 1 + 0 + 0 = 1. No carry is A~ 1 + 0 + 0 =1 H$moB© hm{gb ZhtŸ&
obtained:
Carry → 1 hm{gc
1 0 1
+ 0 0 1
1 0
Now, add 1 and 0 to obtain 1. A~ 1 d 0 H$mo Omo‹S>Zo na 1 {‘boJmŸ&