Page 267 - FUNDAMENTALS OF COMPUTER

NPP

NPP Number System, Boolean Algebra and Logic Circuits 267

1 1 10 1
− 11 01 0
+ 0 0011
The difference is positive because no bor- My±{H$ A§V _| CYma H$s Amdí`H$Vm Zht h¡, Bg{bE
row is needed at the end. CÎma YZmË_H$ h¡Ÿ&
3.30 Binary Multiplication (Unsigned 3.30 ~mBZar JwUZ (AÝgmBÝS> B§Q>rOg©)
Integers)
One way to multiply unsigned binary num- ~mBZar g§»`mAm| H$m JwUm d¡go hr {H$`m Om gH$Vm
bers is exactly similar to the decimal multipli- h¡ O¡go Xe_bd _| {H$`m OmVm h¡Ÿ&
cation.
Consider the following example: {ZåZ CXmhaU H$mo XoImo…

10 1
× 1 10
0 00
10 1 ×
10 1 ××
1 111 0

Problem 3.78 àíZ 3.78
Multiply the following unsigned binary {ZåZ AÝgmBªS> ~mBZar g§»`mAm| H$m JwUm H$amo …
numbers:
(a) 1 0 11 and 1100 (b) 11 0 1 and 1010
Solution: hc:

(a) 10 1 1 (b) 10 1 1
× 1 100 × 11 01
00 00 1 0 10
00 00 × 1 10 1 ×
10 1 1 ×× 00 00 ××
10 1 1 ×× × 1 10 1 ×× ×
1 0 00 0 1 00 1 00 00 0 1 0

But in the computer circuits, the basic idea bo{H$Z H$åß`yQ>a Ho$ n[anW _| JwUm H$mo ~ma-~ma `moJ
of successive addition is used to implement the H$aHo$ g§nÝZ {H$`m OmVm h¡Ÿ& ZrMo {bIo CXmhaU H$mo
multiplication. Consider the following example: g_Pmo:

7 × 3 = 7 + 7 + 7
or 7 × 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3