Question

Using a 4-bit 2's complement arithmetic, which of the following additions will result in an overflow?

(i) 1100 + 1100

(ii) 0011 + 0111

(iii) 1111 + 0111

• A. (i) and (iii) only
• B. (ii) only
• C. (i) only
• D. (iii) only

Answer 1

The correct option is B (ii) only

Overflow in 2's complement arithmetic occur when:

1. There is carry from MSB but no carry come on MSB.

2. There is a carry on MSB but no carry come outside from MSB

$i.e.,C_{out}⨁C_{in}=1$

So,

1 1 1
0 0 1 1
0 1 1 1

1 0 1 0


No overflow since:

$C_{out}⨁C_{in}=0$

1
0 0 1 1
0 1 1 1

1 0 0 1


Overflow since:

$C_{out}⨁C_{in}=1$

1 1 1
1 1 1 1
0 1 1 1

1 0 1 1 0


No overflow since:

$C_{out}⨁C_{in}=0$

Note: Overflow condition $C_{out}⨁C_{in}$