16-bit ripple carry adder is constructed using identical full adders.
Duration: 4 min
A 16-bit ripple carry adder is constructed using identical full adders. Each full adder requires 4 ns to compute the sum output. If the total time taken for 16-bit addition is 67 ns, determine the time taken by each full adder to compute the carry output.
- A.
5 ns
- B.
6 ns
- C.
7 ns
- D.
8 ns
Attempted by 85 students.
Show answer & explanation
Correct answer: A
Answer: The carry output delay per full adder is 4.2 ns (approximately).
Reasoning: In the worst case the input carry must ripple through 15 full adders before the most significant bit (MSB) sum is produced. Let t_c be the carry delay per full adder and t_s be the sum delay.
Number of carry-ripple stages before the MSB sum = 16 − 1 = 15.
Given sum delay t_s = 4 ns, total worst-case delay = 15 * t_c + t_s.
Set up and solve: 15 * t_c + 4 = 67 → 15 * t_c = 63 → t_c = 63 / 15 = 4.2 ns.
Note: None of the provided choices equals 4.2 ns. The closest listed value is 5 ns, but selecting 5 ns would overestimate the carry delay (it yields a total of 15 * 5 + 4 = 79 ns), so the calculated value 4.2 ns is the correct result.
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