Page 261 - FUNDAMENTALS OF COMPUTER

NPP

NPP Number System, Boolean Algebra and Logic Circuits 261

01100

But Sometimes it is required to represent a
positive signed number with greater number of
bits. In that case extra zeros must be inserted
before magnitude bits. 8-bit representation of +12
would be:
00001100
Three zeros inserted are underlined.
From representation of +12 we can obtain
representations of -12 in 8 bit :
1. Signed-magnitude representation: just
complement sign bit :

10001100
2. Signed- 1's complement representation 1's
: complement all the bits including sign bit:
11110011
3. Signed - 2's complement representation 2's
can be obtained from +12 by taking 2's 2's
complement of it including sign bit :
11110100

Problem 3.74 àíZ 3.74
Represent following decimal numbers
using 8-bit binary equivalent :
(a) +14 (b) +25 (c) –17 (d) –63
Solution: hc:
(a) +14 can be represented only in one way - (a)
signed magnitude representation:
00001110
Three zeros are inserted before magnitude
to make eight bit representation.
(b) + 25 is a positive integer and every positive (b)
Integer has a unique representation;
signed-magnitude only: 00011001

(11001 is magnitude in binary.)