A computer uses 8-bit 2's complement representation. Which of the following operations will cause overflow?

Question

A computer uses 8-bit 2's complement representation.

Which of the following operations will cause overflow?

1. A. 01010101 + 00110011
2. B. 10011001 + 10101010
3. C. 01111111 + 00000001
4. D. 11110000 + 00010000

This question was dropped from the final answer key, so it has no correct option — marks were awarded to all candidates.

Detailed Solution & Explanation

This question was discarded and no marks were awarded for it. It is reproduced here for practice, with a full explanation of why it could not be answered as set.

Key Points

• In 8-bit 2's complement representation, the range of values is −128 to +127. Overflow occurs when the result of an addition falls outside this range.
• Working through each option:

• Three of the four options — A, B and C — all cause overflow, while the question asks for a single one. The question was therefore defective as framed, and the Board rightly discarded it.

Additional Information

• How to read an 8-bit 2's complement number:
  • If the most significant bit is 0, the number is positive and read directly.
  • If the most significant bit is 1, the number is negative; its magnitude is found by inverting all bits and adding 1.
  • Example: $10011001$ → invert to $01100110$ → add 1 → $01100111 = 103$, so the value is −103.
• The overflow rules for signed addition:
  • Adding two positive numbers and obtaining a negative result signals overflow.
  • Adding two negative numbers and obtaining a positive result signals overflow.
  • Adding numbers of opposite signs can never overflow — which is exactly why option D is safe.
• Why 2's complement is used: it represents zero uniquely, and allows subtraction to be performed by the same adder circuit as addition, so no separate subtraction hardware is needed.
• Ranges by width: 8-bit gives −128 to +127; 16-bit gives −32,768 to +32,767; in general $n$ bits give $-2^{n-1}$ to $2^{n-1} - 1$.