The addition of 4-bit, two's complement, binary numbers 1101 and 0100 results in
20062009
The addition of 4-bit, two's complement, binary numbers 1101 and 0100 results in
- A.
0001 and an overflow
- B.
1001 and no overflow
- C.
0001 and no overflow
- D.
1001 and an overflow
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Correct answer: C
Step 1: Interpret the numbers as 4-bit two's complement: 1101 = -3, 0100 = +4.
Step 2: Add them in decimal: -3 + 4 = +1.
Binary addition: 1101 + 0100 = 10001 (a 5-bit result). Discard the extra carry-out and take the lower 4 bits: 0001.
Interpretation: 0001 represents +1 in 4-bit two's complement.
Overflow rule: Overflow in two's complement occurs when adding two numbers with the same sign gives a result with a different sign. Here the operands have opposite signs, so overflow does not occur.
Answer: 0001 and no overflow.
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