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258 Fundamentals of Computers NPP

3.26 Representation of Binary Integers 3.26 ~mBZar nyUmªH$m| H$m à{V{Z{YËd
(Unsigned and Signed Integers) (AZgmBÝS> VWm gmBÝS> nyUmªH$)
There are two types of Binary Integers : Xmo àH$ma Ho$ ~mBZar nyUmªH$ Cn`moJ _| AmVo h¢ …
1. Unsigned Binary Integers . 1. AZgmBÝS> ~mBZar nyUmªH

2. Signed Binary Integer 2. gmBÝS> ~mBZar nyUmªH$
Unsigned Binary Integer AZgmBÝS> ~mBZar nyUmªH$
In this type of integer, there is no sign bit. Bg_| {MÝh hoVw H$moB© {~Q> Zht hmoVr Ÿ& gmar {~Q>|
All the bits show magnitude of the integer. For g§»`m H$m n[a_mU Xem©Vr h¡ Ÿ& O¡go Xe_bd nyUmªH$ 12
example, decimal 12 is represented as (1100) .
2
H$mo ~mBZar _| (1100) Ho$ ê$n _| Xem© gH$Vo h¢ Ÿ&
2
Signed Binary Integers gmBÝS> ~mBZar nyUmªH$
In this type of integers, one bit is used to Bg àH$ma Ho$ nyUmªH$ _| EH$ {~Q> {MÝh Xem©Vr h¡ Ÿ&
indicate the sign of the binary number. This bit `h {~Q> MSB (_moñQ> {gp½Z{\$H|$Q> {~Q>) hmoVr h¡ Ÿ& `h
is usually MSB (Most Significant Bit). The MSB {~Q> Bg àH$ma go Xmo {MÝhm| H$mo Xem©Vr h¡ …
has following interpretation:
0 → Positive Sign
1 → Negative Sign.
Signed Integers can further be divided into BÝh| Xmo dJm] _| ~m±Q>m Om gH$Vm h¡ …
two categories:
Positive Signed Integers : These numbers YZmË_H$ gmBÝS> nyUmªH$ … BÝh| MSB Ho$ eyÝ` hmoZo
are identified with the help of MSB which is go nhMmZm Om gH$Vm h¡ Ÿ& Bg àH$ma H$s g§»`mAm| H$m
equal to zero. Positive Integers have only unique EH$ hr àH$ma H$m à{V{Z{YËd hmoVm h¡, {Ogo gmBÝS>-
representation which is called as Signed-
Magnitude Representation. _o{¾Q²>`yS> à{V{Z{YËd ({MÝh- n[a_mU) H$hVo h¢ Ÿ&
In this representation, MSB(0) shows Bg à{V{Z{YËd _| EH$ {~Q> (0) YZmË_H$ {MÝh
positive sign and the remaining bits show Xem©Vr h¡ VWm ~mH$s {~Q>| n[a_mU Xem©Vr h¢ Ÿ& O¡go + 12
magnitude. For example, +12 can be H$mo Bg àH$ma go Xem©`m Om gH$Vm h¡:
represented as :

+ 12

0 1100

Sign Bit Magnitude Bits
Thus, +12 has only one representation: AWm©V² + 12 H$m EH$ hr à{V{Z{YËd h¡ …
01100