Adders — hardware count: An m-bit parallel binary adder (ripple or look-ahead per bit) contains how many full adder stages?

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:

• We consider an m-bit adder for two m-bit operands.
• Each bit requires sum and carry processing.
• Half adders are insufficient when a carry-in must be accommodated.

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.