Page 318 - FUNDAMENTALS OF COMPUTER

318 Fundamentals of Computers NPP

3.47 Binary Adder/Subtractor 3.47 ~mBZar ES>a/g~Q´>oŠQ>a
Adder/Subtractor is a combinational logic ES>a/g~Q´>oŠQ>a n[anW Omo‹S>Zo VWm KQ>mZo XmoZm| Ho$
circuit which can add as well as subtract two H$m`© _| AmVm h¡, Bg{bE Bgo ES>a/g~Q´>oŠQ>a H$hVo h¢Ÿ&
binary numbers. For subtraction it, uses 2's KQ>mZo hoVw 2's H$m°påßb_|Q {d{Y H$m Cn`moJ H$aVo h¢Ÿ& KQ>mZo
complement method. The subtraction is Ho$ ~OmE {H$gr g§»`m H$m 2's H$m°påßb_|Q Omo‹S> {X`m OmVm
equivalent to addition of 2's complement.
Consider the following circuit: h¡Ÿ& {ZåZ n[anW H$mo XoImo…

A 3 A 2 A 1 A 0

B 3 B 2 B 1 B 0
SUB

F.A.
C 3
C 4 F.A. NPP C 2 F.A. C 1 F.A. C 0
S 3 S 2 S 1 S 0

X 4 X 3 X 2 X 1 X 0
When SUB = 0 first Full Adder will add A 0 O~ SUB = 0 hmoVm h¡ V~ àW_ \w$b ES>a A VWm
0
and B , the second Full Adder will add A , B 1 B Omo‹S>Vm h¡ Ÿ& Bgr Vah ~mH$s \w$b ES>a _| hm{gb d
0
1
0
and the carry C 1 of first Full Adder. It works as {~Q>m| H$mo Omo‹S>Vo h¢ Ÿ& AV… `h ES>a H$m H$m`© H$aVm h¡&
a binary adder. When SUB = 1, the second binary bo{H$Z O~ SUB = 1 hmoVm h¡, Vmo gmao \w$b ES>am| Ho$
number B B B B is inverted. And the outputs AmCQ>nwQ> H$mo Bg àH$ma go {bIm Om gH$Vm h¡ …
3 2 1 0
of Full Adders would give
A 3 A 2 A 1 A 0
+ B 3 B 2 B 1 B 0

+ 1

This is addition of 2's Complement of AV… h_ B B B B Ho$ 2's H$m°påßb_|Q H$mo
3 2 1 0
B B B B to A A A A . It is equivalent to A A A A _| Omo‹S> aho h¢& AWm©V² B B B B H$mo
1
0
3 2 1 0
2
3
1
0
2
3 2 1 0
3
subtracting first number from second. When A A A A _| go KQ>m aho h¢Ÿ& AV… SUB = 1 go
SUB = 1 this circuit works as a subtractor and 3 2 1 0
when SUB = 0 it works as an adder. g~Q´>oŠQ>a H$m VWm SUB = 0 go ES>a H$m n[anW àmá hmo
ahm h¡…