Discussion
How many flip-flops are required to build a modulus-16 binary counter?
Answer: D
Correct answer: 4
A binary counter with \( n \) flip-flops passes through \( 2^{n} \) distinct states, so a modulus-16 counter needs \[ 2^{n} = 16 \quad\Rightarrow\quad n = 4. \] Each flip-flop stores one bit, and four bits represent the sixteen values 0000 to 1111 - decimal 0 to 15. The general rule is worth remembering in both directions: for a required modulus \( N \), the number of flip-flops is the smallest \( n \) with \( 2^{n} \ge N \). A decade counter of modulus 10 therefore still needs four flip-flops, and the six unused states are removed by feedback that resets the counter at a count of ten. Counters divide as well as count: a modulus-16 counter’s most significant output is the clock frequency divided by 16, which is why they are used as frequency dividers. An asynchronous or ripple counter clocks each stage from the previous one and is simpler but slower; a synchronous counter clocks every stage together and avoids the accumulated delay.
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