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?
1100 + 1100
0011 + 0111
1111 + 0111
- A.
(i) only
- B.
(ii) only
- C.
(iii) only
- D.
(i) and (iii) only
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Correct answer: B
Key idea: Overflow in two's complement occurs when adding two numbers with the same sign produces a result with the opposite sign. For 4-bit two's complement the representable range is -8 to +7.
1100 + 1100: 1100 is -4, so -4 + -4 = -8. The 4-bit result is 1000, which represents -8, so there is no overflow.
0011 + 0111: 0011 is 3 and 0111 is 7, so 3 + 7 = 10. The 4-bit result is 1010 (interpreted as -6), which shows overflow because the true sum exceeds the maximum representable +7.
1111 + 0111: 1111 is -1 and 0111 is 7, so -1 + 7 = 6. The 4-bit result is 0110 (6), so there is no overflow.
Final answer: Only the addition 0011 + 0111 results in overflow.