Question

The following binary numbers are 4-bit 2's complement binary numbers. Which of the following operations generate overflow? Justify your answers by translating the operands and results into decimal.

a)0011+1100
b)0111+1111
c)1110+1000
d)0110+0010

Answer 1

In the context of 4-bit 2's complement binary numbers, only operation c (1110 + 1000) generates overflow, as the result cannot be represented within the limits of 4 bits.option c.

Step-by-step explanation:

The question addresses the concept of overflow in binary addition, particularly in the context of 4-bit 2's complement numbers. Overflow occurs when the result of an addition cannot be represented with the number of bits available. To determine this, we need to understand and apply the rules of binary addition and 2's complement representation.

Let's analyze each operation:

1. 0011 + 1100: In decimal, this is 3 + (-4) which equals -1. This operation does not generate overflow since the result can be represented in 4 bits.
2. 0111 + 1111: In decimal, this is 7 + (-1) which equals 6. This operation also does not generate overflow.
3. 1110 + 1000: In decimal, this is -2 + (-8) which equals -10. However, -10 cannot be represented in 4-bit 2's complement, thus this operation generates overflow.
4. 0110 + 0010: In decimal, this is 6 + 2 which equals 8, and can be represented in 4 bits with no overflow.

Therefore, only operation c) 1110 + 1000 generates overflow.