Page 287 - FUNDAMENTALS OF COMPUTER

NPP

NPP Number System, Boolean Algebra and Logic Circuits 287

Solution:

(a) (+25) – (+25) represent both numbers (a) XmoZm| H$mo 8-{~Q>m| Ho$ gmBÝS> _op½ZQ²>`yS> _|
in 8-bit sign-magnitude form : {bIZo na
(00011001) – (00011001)
Take 2's complement of subtrahend. KQ>H$ H$m 2's H$m°påßb_|Q> bmoŸ& (-) Ho$ ñWmZ na
Replace (–) with (+) and add. Neglect any end (+) {bImo VWm Omo‹S>moŸ& A§{V_ hm{gb H$mo N>mo‹S>mo…
carry.
0 0 0 1 1 0 0 1
+ 1 1 1 0 0 1 1 1
0 0 0 0 0 0 0 0
end 1
carry
Therefore, result is 00000000 and its AV… n[aUm_ 00000000 h¡ {OgH$m Xe_bd 0
decimal number is 0. Thus, hmoVm h¡… AV…
(+ 25) – (+ 25) = 0
(b) (+43) – (–20), Signed-Magnitude (b) (+43) – (–20), ( + 43) H$m gmBÝS> _op½ZQ²>`yS
representation of (+43) is : Vwë` Bg àH$ma h¡…
0 0 1 0 1 0 1 1
Signed - 2's Complement representation (-20) H$m gmBÝS> 2's H$m°påßb_|Q> Vwë` Bg àH$ma
(–20) is (Which is obtained by 2’s complement h¡… (Omo {H$ +20 Ho$ Vwë¶ H$m 2’s H$m°påßb‘|Q> boZo na
of + 20)
àmßV hmoJm)
1 1 1 0 1 1 0 0
Take 2's complement of subtrahend (–20) (- 20) H$m 2's H$m°påßb_|Q> hmoJm…
which will be
0 0 0 1 0 1 0 0
Replace (–) with (+) and add: (-) Ho$ ñWmZ na (+) {bIH$a Omo‹S>mo…
0 01 01 01 1
+ 000 1 0 1 00

00 111111

MSB is 0 which shows that the result is My±{H$ MSB eyÝ` h¡ AV… n[aUm_ YZmË_H$ h¡, Omo
positive and it is +63. Therefore: + 63 hmoVm h¡ Ÿ& AV…
(+43) – (–20) = (+63)

Problem 3.82 àíZ 3.82
Perform 2's complement addition: 2's H$m°påßb_|Q> go Omo‹S>mo…
(a) (+32) + (–14) (b) (–47) + (–31)