Interpreting counter modulus A counter with modulus 16 will function as which kind of frequency divider?

Introduction / Context:The modulus (MOD) of a counter is the number of distinct states in its counting cycle. When used as a frequency divider, the output signal that toggles once per full cycle divides the input clock by the modulus. Understanding this relationship allows quick estimation of division factors in timing chains.

Given Data / Assumptions:

• Counter modulus: 16 → 16 unique states per cycle.
• Each complete cycle corresponds to one output repetition.
• Assume a single output that indicates cycle completion (for example, decoded terminal count or MSB patterns).

Concept / Approach:For N distinct states, the counter advances one state per clock pulse and repeats every N pulses. Therefore, the fundamental repetition period corresponds to dividing the clock frequency by N. With MOD=16, the division factor is 16, producing an output with frequency f_out = f_clk / 16 under standard use.

Step-by-Step Solution:

Verification / Alternative check:Consider a synchronous 4-bit binary counter: its MSB toggles at f_clk/16, and its state sequence length is 16, matching the modulus definition.

Why Other Options Are Wrong:

• divide-by-8/32/64: These correspond to moduli 8/32/64 respectively, not 16.

Common Pitfalls:Confusing the MSB toggle rate with the total modulus in unusual wiring; generally, the modulus dictates the fundamental division ratio.

Final Answer:divide-by-16 counter