Counting on Digital Logic Notebook

Ripple Counters

Mon, 01 Jan 0001 00:00:00 +0000

Ripple Counters#

A ripple counter is the simplest way to count in hardware: a chain of toggle flip-flops in which each stage’s output clocks the next. The first stage toggles on the input clock, dividing it by two; its output clocks the second stage, dividing by two again; and so on. With n stages the chain counts from 0 to 2ⁿ−1 in binary and divides the input frequency by 2ⁿ — all from flip-flops and a wire, no logic gates and no software.

Synchronous Counters

Mon, 01 Jan 0001 00:00:00 +0000

Synchronous Counters#

A synchronous counter fixes the ripple counter’s central flaw by clocking every flip-flop from the same clock at the same time. There is no ripple: on each edge all stages that need to change do so together, so the count is valid all at once and the counter runs as fast as a single stage allows.

Knowing When to Toggle#

If every flip-flop shares the clock, each one needs to be told in advance whether to flip on the coming edge. That is the job of a little combinational logic: a stage toggles only when all the stages below it are already 1. Stage 0 toggles every edge; stage 1 toggles when bit 0 is 1; stage 2 toggles when bits 0 and 1 are both 1 — a chain of AND gates feeding each flip-flop’s toggle enable. The flip-flops still all fire on the same edge; the logic just decides which ones act.

Frequency Dividers

Mon, 01 Jan 0001 00:00:00 +0000

Frequency Dividers#

A frequency divider produces a slower clock from a faster one, and a counter is already a frequency divider — the two are the same circuit viewed two ways. Every toggle flip-flop stage halves the frequency, so an n-stage counter divides its input by 2ⁿ while it counts. Deriving usable clocks this way is one of the most common jobs a counter does.

Dividing by Two, by 2ⁿ, and by N#

Dividing by a power of two is free: tap the output of the right stage of a binary counter. Stage 0 gives ÷2, stage 3 gives ÷16, and so on.

Ring & Johnson Counters

Mon, 01 Jan 0001 00:00:00 +0000

Ring & Johnson Counters#

Ring and Johnson counters count differently from a binary counter: instead of incrementing a number, they circulate a pattern around a shift register. They trade code efficiency for something valuable — outputs that are already decoded and free of glitches.

Ring Counter#

A ring counter is a shift register with its last output fed straight back to its first input. Seed it with a single 1 and that one bit walks around the loop: 1000 → 0100 → 0010 → 0001 → 1000. With N flip-flops it has N states, and exactly one output is active at a time — a one-hot sequence. Because each output is a decoded state, no decoding logic is needed and there are none of the ripple-counter decoding glitches: the outputs are already clean, one-per-step control signals. That makes ring counters ideal for sequencers, stepper-motor phase drives, and LED chasers.