Page 260 - FUNDAMENTALS OF COMPUTER

NPP

260 Fundamentals of Computers NPP

Signed - 2's Complement Representation gmBÝS> 2's H$m°påßb_|Q> à{V{Z{YËd … Bg_| ^r MSB
: In this representation also MSB is 1. Remaining Ho$ ñWmZ na 1 hmoVm h¡ Omo F$U {MÝh Xem©Vm h¡ Ÿ& ~mH$s
bits are 2's Complement of the magnitude. For H$s {~Q>| n[a_mU H$m 2's H$m°påßb_|Q>> Xem©Vr h¢ & O¡go,
example, –12 can be represented as:
-12 H$mo Bg Vah go Xem©`m Om gH$Vm h¡ …

12

1 0100

Sign Bit 1’s Complement of Magnitude
Thus –12 in this representation is 10100. AWm©V² - 12 H$mo Bg_| Eogm {bIm Om gH$Vm h¡ …

10100
From the above example it is clear that CnamoŠV dU©Z go ñnï> hmoVm h¡ {H$ - 12 H$m
representation of -12 can be obtained from +12 à{V{Z{YËd +12 Ho$ à{V{Z{YËd go Bg àH$ma ^r {ZH$mb
with help of following procedure :
gH$Vo h¢ …
1. Signed-Magnitude Representation- 1. (gmBÝS>-_op½ZQ²>`yS>)
+ 12 – 12

01100 11100
Just complement sign bit. {g\©$ {MÝh dmbr {~Q> (MSB) H$m H$m°påßb_|Q> H$am|&
2. Signed - 1's Complement Representation- 2. (gmBÝS>- 1's H$m°påßb_|Q>) gånyU© g§»`m H$m 1's
Complement all the bits including sign-bit : H$m°påßb_|Q> boZo go + 12 go - 12 H$m à{V{Z{YËd
àmá hmoVm h¡ Ÿ&
+ 12 – 12

01100 10011
3. Signed - 2's Complement Representation: 3. (gmBÝS> 2's H$m°påßb_|Q>>) gånyU© g§»`m {Og_| {MÝh
Take 2's Complement of the complete dmbr {~Q> ^r em{_b h¡, H$m 2's H$m°påßb_|Q> boVo
number including sign bit h¢ Ÿ&

+ 12 – 12

01100 10100

3.27 8-bit representation of signed 3.27 gmBÝS> nyUmªH$m| H$m bit _| à{V{Z{YËd
numbers
Consider an example of +12. It can be
represented using 5-bits as follows: