Project ForgeDigital Logic
Combinational & Sequential Circuits
GATE 2016
Hard
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 ____.
-1
Explanation
The longest latency occurs when the carry must ripple through all 8 bit positions. A=1 is 00000001. Adding B=−1 (11111111) gives 1+(−1)=0, requiring the carry to propagate through every single bit position (each bit position generates a carry into the next), producing the maximum-length ripple chain.
Source: GATE CS 2016 (Session 2 / Set B) (2016)
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