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 _________________ .
Attempted by 267 students.
Show answer & explanation
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.
A video solution is available for this question — log in and enroll to watch it.