The binary representation of the number has two
parts
•
The MSB is used to denote the sign (+ve or -ve) of the
number
•
The remaining bits signify the magnitude of the
number
•
(+ 123)
10
= (01101)
2
•
(- 123)
10
= (11101)
2
Reference: Principles of Digital Design,
Gajski
6

Representation of negative numbers 2/3
•
Suppose we want to add two numbers in this
representation <s
1
,m
1
> and <s
2
,m
2
>
–
First check the sign bits s
1
and s
2
•
If both are the same, then add the magnitudes and the
result has the same sign as s
1
and s
2
•
If both bits are different and
–
The magnitude is the same, then the result is zero
–
Otherwise, subtract the smaller magnitude from the larger
and the result has the sign of the larger magnitude
Reference: Principles of Digital Design,
Gajski
7

Representation of negative numbers 3/3
•
Suppose we use 8 bits for each number
Reference: Principles of Digital Design,
Gajski
8
(11111011)
2
+ (00000011)
2
= ?
Both sign bits are different, so the magnitude of
the result is: 1111011 – 0000011 = 1111000
We keep the sign of the larger magnitude
Ans: (11111000)
2
= (- 120)
10

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- Fall '18
- Eric Swartz