Question

A mod-10 counter requires

• A. \(2\) flip-flops
• B. \(3\) flip-flops
• C. \(4\) flip-flops
• D. \(10\) flip-flops

Hint:

For a mod-\(N\) counter, \[ \boxed{ n=\left\lceil\log_2N\right\rceil } \] where \(n\) is the minimum number of flip-flops required.

Answer 1

The Correct Option is C

Step 1: Use the flip-flop requirement formula. The minimum number of flip-flops required is \[ 2^n \geq N, \] where \(N\) is the modulus. Here, \[ N=10. \]

Step 2: Determine the value of \(n\). Since \[ 2^3=8<10, \] and \[ 2^4=16\ge10, \] the required number of flip-flops is \[ \boxed{4.} \] Therefore, \[ \boxed{(C)} \] is the correct answer.