Page 259 - FUNDAMENTALS OF COMPUTER

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NPP Number System, Boolean Algebra and Logic Circuits 259

Negative Integers : These numbers can be F$UmË_H$ nyUmªH$ … BZH$mo h_ MSB _| 1 hmoZo go
identified if the MSB is 1. But there are three nhMmZ gH$Vo h¢ naÝVw àË`oH$ F$UmË_H$ nyUmªH$ H$mo VrZ
possible ways with which negative Binary
integers can be represented : VarH$m| go Xem©`m Om gH$Vm h¡ …
1. Signed-Magnitude Representation. 1. gmBÝS>- _o¾rQ²>`yS>
2. Signed- 1's Complement Representation. 2. gmBÝS> - 1's H$m°påßb_|Q>

3. Signed- 2's Complement Representation. 3. gmBÝS> - 2's H$m°påßb_|Q>

Signed-Magnitude Representation : In gmBÝS>-_op½ZQ²>`yS> à{V{Z{YËd- Bg àH$ma Ho$
this type of Representation MSB is 1 and à{V{Z{YËd _| MSB 1 hmoVm h¡, Omo F$U H$m {MÝh Xem©Vm
remaining bits show the magnitude. e.g. –12
can be represented as : h¡ VWm ~mH$s {~Q>| n[a_mU Xem©Vr h¢ Ÿ& O¡go - 12 H$mo Eogo
Xem©`m Om gH$Vm h¡:

12

1 1100

Sign Bit Magnitude Bits

Therefore –12 in this representation will AV… - 12 H$mo Bg àH$ma go {bIm Om gH$Vm h¡
be written as 11100.
11100.
Signed - 1's Complement Representation: gmBÝS> - 1's H$m°påßb_|Q> à{V{Z{YËd … Bg àH$ma
In this representation, there is a sign bit which Ho$ à{V{Z{YËd _| MSB 1 hmoVr h¡ Omo F$U {MÝh Xem©Vr h¡
is equal to 1 (MSB). Remaining Bits are 1's VWm ~mH$s {~Q>| n[a_mU H$m 1's H$m°påßb_|Q> hmoVr h¢ Ÿ& O¡go
Complement of magnitude. For example, –12
can be represented as : - 12 H$mo Bg Vah go Xem©`m Om gH$Vm h¡ …

12

1 0011

Sign Bit 1’s Complement of Magnitude

Thus, –12 in this representation is 10011. AV… - 12 Bg à{V{Z{YËd _| Eogo {bIm OmEJm …
10011.