Building wider adders — cascading 4-bit adders to form a 16-bit adder When constructing a 16-bit adder from 4-bit adder ICs, what is required?

Introduction / Context:Multi-bit addition is often implemented by cascading smaller adder blocks (e.g., 4-bit 74xx adders). Understanding how many ICs are needed and how to connect their carry signals is fundamental to designing arithmetic datapaths.

Given Data / Assumptions:

• Target width: 16 bits.
• Available building block: a 4-bit adder with carry-in (Cin) and carry-out (Cout).
• Ripple-carry architecture unless a separate carry-lookahead is used.

Concept / Approach:

Divide the 16-bit vectors into four 4-bit slices: bits [3:0], [7:4], [11:8], [15:12]. Each slice uses one 4-bit adder. Chain the carry: Cout from the less significant slice feeds Cin of the next slice. Optionally tie Cin of the least significant slice to 0 for simple addition or to 1 for add-with-carry (increment).

Step-by-Step Solution:

Verification / Alternative check:

This is the canonical ripple-carry adder construction and matches vendor datasheets and textbook examples. Carry-lookahead units can accelerate the chain but still maintain the same basic slice count and carry connectivity.

Why Other Options Are Wrong:

• 16 adders: confuses bit count with IC count.
• 4 adders only: incomplete—omits the crucial carry-chain requirement.
• Carry chain only: incomplete—must also state four adders.
• 8 adders, no carry chain: both incorrect.

Common Pitfalls:

• Forgetting to propagate carry, yielding wrong sums at higher slices.
• Mixing slice order so that carries run backward.

Final Answer:

requires 4 adders and the connection of the carry out of the less significant adder to the carry-in of the next significant adder.