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

To determine if an addition operation generates overflow in 2's complement binary numbers, we need to check the signs of the operands and the result. The leftmost bit of the operands and the result indicate the sign. If the leftmost bits of the operands differ from the leftmost bit of the result, overflow occurs.

Step-by-step explanation:

To determine if an addition operation generates overflow in 2's complement binary numbers, we need to check the signs of the operands and the result. In 4-bit 2's complement binary representation, the leftmost bit represents the sign. If the leftmost bits of the operands are different from the leftmost bit of the result, overflow occurs. Let's analyze the given operations:

1. a) 0011 + 1100 = 1111. The leftmost bits of the operands (0 and 1) are different from the leftmost bit of the result (1), so overflow occurs.
2. b) 0111 + 1111 = 01110. The leftmost bits of the operands (0 and 1) are the same as the leftmost bit of the result (0), so no overflow occurs.
3. c) 1110 + 1000 = 0110. The leftmost bits of the operands (1 and 1) are the same as the leftmost bit of the result (0), so no overflow occurs.
4. d) 0110 + 0010 = 1000. The leftmost bits of the operands (0 and 0) are the same as the leftmost bit of the result (1), so no overflow occurs.

In decimal, the translations are:

• a) 3 + (-4) = -1
• b) 7 + (-1) = 6
• c) (-2) + 8 = 6
• d) 6 + 2 = 8