Difficulty: Easy
Correct Answer: m full adders
Explanation:
Introduction / Context:
Parallel adders implement multi-bit addition by cascading single-bit full adders. Each stage handles a bit position and propagates/produces carry signals. Knowing the stage count is essential for estimating delay, area, and power.
Given Data / Assumptions:
Concept / Approach:
A full adder computes sum and carry from A_i, B_i, and carry_in. Since every bit position has these three inputs (except perhaps the LSB if designed with a half adder when carry_in is assumed 0), the canonical design uses m full adders to allow a carry chain across all bits. Ripple, carry-look-ahead, or other schemes still allocate one full-adder cell per bit.
Step-by-Step Solution:
Map one full-adder cell to each of the m bit positions.Account for carry propagation across all stages.Therefore, total full adders = m.
Verification / Alternative check:
Logic diagrams of 4-bit adders show 4 full adders; extending to m bits generalizes linearly.
Why Other Options Are Wrong:
(m+1) and (m−1) miscount; m/2 would only cover half the bits.
Common Pitfalls:
Using a half adder at LSB is a special case only when carry_in is guaranteed 0; the general parallel adder uses m full adders.
Final Answer:
m full adders.
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