Discussion
Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
Answer: B
Overflow occurs for R1 = 1100 and R2 = 1010.
In 4-bit two's complement the range is −8 to 7. Overflow happens when two numbers of the same sign give a result outside that range, which shows as a result with the opposite sign.
1100 is −4 and 1010 is −6. Their sum is −10, below −8; the 4-bit result is 0110, a positive number, so the addition overflows.
The others stay in range: 1011 + 1110 is −5 + (−2) = −7; 0011 + 0100 is 3 + 4 = 7; 1001 + 1111 is −7 + (−1) = −8, the most negative value, still representable.
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