How many full and half-adders are required to add 16-bit numbers? A. 8 half-adders, 8 full-adders B. 1 half-adders, 15 full-adders C. 16 half-adders, no full-adders D. 4 half-adders, 12 full-adders E. None of the above

The correct answer is $\boxed{\text{D. 4 half-adders, 12 full-adders}}$.

A half-adder is a digital circuit that adds two single-bit binary numbers and produces a sum and a carry bit. A full-adder is a digital circuit that adds two single-bit binary numbers and a carry bit, and produces a sum and a carry bit.

To add two 16-bit numbers, we can use a cascade of half-adders and full-adders. The first stage of the cascade would be four half-adders, one

for each of the four least significant bits of the two numbers. The second stage would be four full-adders, one for each of the four pairs of bits that are the sum of the two least significant bits and the carry bit from the first stage. The third stage would be four full-adders, one for each of the four pairs of bits that are the sum of the two pairs of bits from the second stage and the carry bit from the first stage. The fourth and final stage would be one full-adder, which would add the two carry bits from the third stage to produce the sum of the two 16-bit numbers.

In total, we would need 4 half-adders and 12 full-adders to add two 16-bit numbers.

Option A is incorrect because it would require 8 half-adders and 8 full-adders, which is more than necessary.

Option B is incorrect because it would require 1 half-adder and 15 full-adders, which is more than necessary.

Option C is incorrect because it would require 16 half-adders and no full-adders, which is not possible.

Option E is incorrect because it is not one of the given options.