Consider an eight-bit ripple-carry adder for computing the sum of A and B,…

2016

Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _________________ .

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Correct answer: -1

Answer: -1

Reason: An eight-bit two's-complement representation of -1 is 11111111, and A = +1 is 00000001. Adding these produces a carry from the least significant bit. For every higher bit, B has a 1 while A has a 0, so each stage satisfies the propagate condition and forwards the carry to the next stage. The carry therefore ripples through all eight bit positions, producing the longest possible stabilization latency.

  • LSB: 1 + 1 generates a carry into the next bit.

  • Bits 1–7: each has A=0 and B=1, so each stage propagates the incoming carry.

  • Result: carry travels through all 8 stages, giving the worst-case (longest) ripple-carry latency.

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