Using a 4-bit 2’s complement arithmetic, which of the following additions will…
2004
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) only
- B.
(ii) only
- C.
(iii) only
- D.
(i) and (iii) only
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Correct answer: B
Answer: Only 0011 + 0111 causes overflow.
Key rule: Overflow in two's complement addition occurs when two numbers with the same sign produce a result with the opposite sign (equivalently, when the true sum falls outside the representable range −8 to +7 for 4 bits).
1100 + 1100: 1100 represents −4. Sum = −4 + (−4) = −8, which is representable as 1000 in 4-bit two's complement. No overflow.
0011 + 0111: 0011 is +3 and 0111 is +7. Sum = +10, which is outside the representable range. Binary addition gives 1010 (interpreted as −6), so two positives produced a negative result — this is an overflow.
1111 + 0111: 1111 is −1 and 0111 is +7. Sum = −1 + 7 = +6, representable as 0110. Operands have opposite signs, so no overflow.
Therefore, only 0011 + 0111 results in overflow.
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