A binary ripple counter is designed to count (0)₁₀ to (64)₁₀. Which of the following is/are the number of flip-flops required ...
Q. A binary ripple counter is designed to count (0)₁₀ to (64)₁₀. Which of the following is/are the number of flip-flops required to design the counter?
(A) 6 (B) 7 (C) 4 (D) 5
Solution
A binary ripple counter must count from (0)₁₀ to (64)₁₀, including both endpoints.
Step 1: Calculate the total number of states
Since both 0 and 64 are included, add 1 to the difference:
N = Last value − First value + 1
N = 64 − 0 + 1 = 65 states
N = 64 − 0 + 1 = 65 states
The counter visits every integer from 0 through 64:
0, 1, 2, 3, ..., 63, 64
There are 65 distinct states in total.
Step 2: Calculate the number of flip-flops
Each flip-flop stores one bit. With n flip-flops, the counter can represent 2ⁿ distinct states.
2⁶ = 64 states (not enough)
2⁷ = 128 states (enough)
n = 7 flip-flops