Question E7A04:
How many flip-flops are required to divide a signal frequency by 16?  

Choices:  
A: 4  
B: 6  
C: 8  
D: 16    

Correct Answer is  A: 4  

To divide a frequency by a power of two using flip-flops, each flip-flop divides the frequency by 2. Cascading them multiplies the divide ratio.

Key rule:
$$\text{Divide ratio} = 2^N \quad \Rightarrow \quad N = \log_2(\text{Divide ratio})$$

For divide-by-16:
$$N = \log_2(16) = 4$$
So, 4 flip-flops are required.

Why A (4) is correct:
- Each flip-flop halves the frequency: divide-by-2, then 4, 8, 16 after 4 stages.

Why the others are incorrect:
- B (6): $2^6 = 64$ (would divide by 64)
- C (8): $2^8 = 256$ (would divide by 256)
- D (16): $2^{16} = 65{,}536$ (would divide by 65,536)

Rule of thumb:
- For divide-by-$2^k$, use $k$ flip-flops.
- For non–power-of-two ratios, you need enough flip-flops to cover the count and add reset logic, but for powers of two it’s simply $N = \log_2(\text{ratio})$.