Question

Determine the output frequency of a frequency division circuit which contains 12 flip-flops with an input clock frequency of 20.48 MHz.

• A. \( \text{10.24 kHz} \)
• B. \( \text{05 kHz} \)
• C. \( \text{30.24 kHz} \)
• D. \( \text{15 kHz} \)

Hint:

For a frequency divider circuit built with \( N \) cascaded flip-flops (typically in a ripple counter configuration), the output frequency is always the input frequency divided by \( 2^N \). Remember the powers of 2 (e.g., \( 2^{10} = 1024 \)) to quickly calculate division factors in such problems. Always convert units (MHz to kHz) as needed.

Answer 1

The Correct Option is B

A frequency division circuit containing\( N \)flip-flops typically operates as a ripple counter or a similar sequential circuit that divides the input frequency by\( 2^N \).
Here, the number of flip-flops\( N = 12 \), and the input clock frequency is\( f_{\text{in}} = 20.48 \text{ MHz} \).The division factor is:\[ 2^{12} = 2^{10} \times 2^2 = 1024 \times 4 = 4096 \]The output frequency is:\[ f_{\text{out}} = \frac{f_{\text{in}}}{2^N} = \frac{20.48\ \text{MHz}}{4096} \]Convert MHz to kHz:\[ 20.48\ \text{MHz} = 20480\ \text{kHz} \]Now calculate:\[ f_{\text{out}} = \frac{20480}{4096} = 5\ \text{kHz} \]Thus, the output frequency is\( \boxed{5\ \text{kHz}} \), which matches option (B).