Page 319 - FUNDAMENTALS OF COMPUTER

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NPP Number System, Boolean Algebra and Logic Circuits 319

A 3 A A 1 A 0 B 3 B B B 0
2
1
2

Binary Adder/Subtractor SUB

X 4 X 3 X 2 X 1 X 0
3.48 Half Subtractor 3.48 hm\$ g~Q´>oŠQ>a

Definition: n[a^mfm…
"This is a combinational logic circuit which ""`h dh H$m§{~ZoeZb Vm{H©$H$ n[anW h¢, Omo Xmo
can perform arithmetic subtraction over two {~Q>m| H$mo KQ>mVm h¡ Ÿ&''
bits."
Block Diagram ãcm°H$ S>m`J«m_
A Half subtractor has two inputs A and B EH$ hm\$ g~Q´>oŠQ>a _| Xmo BZnwQ> A d B VWm Xmo
and two output bits Borrow and difference: AmCQ>nwQ> ~moamo d {S>\$a|g hmoVo h¢…

A B Borrow Difference
0 0 0 0 A Borrow
A Half Borrow 0 1 1 1 B
Subtractor
B Difference A-B 1 0 0 1 Difference
1 1 0 0
From the examination of difference it is gË` Vm{bH$m go ñnï> h¡ {H$ Difference H$mo EH$
clear that it can be obtained by XOR gate. The XOR JoQ> H$s ghm`Vm go àmá H$a gH$Vo h¢ Š`m|{H$ EH$
output is zero for similar inputs and output is
1 for dissimilar inputs. That is: XOR JoQ> _| hr A = B hmo Vmo AmCQ>nwQ> eyÝ` AmVm h¡& AV…
difference = A ⊗ B
But Borrow does not follow truth table for na§Vw Borrow {H$gr EH$ JoQ> H$s gË` Vm{bH$m H$m
a single gate. Its expression can be found as : nmbZ Zht H$aVm h¡ Ÿ& gË` Vm{bH$m go ñnï> h¡ {H$
Borrow is 1 only when A = 0 and B = 1. In other Borrow na 1 V^r AmVm h¡ O~ A = 0 Am¡a B = 1 AWdm
words A = and B=1 That means; A = 1Am¡a B = 1 Bgr H$WZ H$mo h_ Eogo {bI gH$Vo
1
Borrow= A .B . With the help of expression of
h¢ Borrow = A . B Difference H$s g‘rH$aU VWm