Redstone circuits/Pulse/pulse divider

Hopper-Loop Pulse Divider

2×(3 + pulse count/2)×3

output pulse: 3 ticks

The bottom-right hopper contains a single item.

Dropper-Hopper Pulse Divider

3×4×2 (24 block volume)
flat

output pulse: (4 × pulse count) ticks

The dropper contains a number of items equal to the pulse count. The bottom-left hopper contains a single item.

Dropper-Dropper Pulse Divider

3×6×2 (36 block volume)
flat

output pulse: (2 × pulse count) ticks

The left dropper contains a number of items equal to the pulse count. The left hopper contains a single non-stackable item.

Inverted Binary Divider / Counter (wide)

3×5×2 (30 block volume)
flat, silent, 3-wide stackable (alternating)

output pulse: 2 off-ticks

This circuit triggers on a 2-tick off-pulse input, and outputs a pulse for every two input pulses. It can be stacked to obtain a divider for any power of 2 (2, 4, 8, 16, etc).

Inverted Binary Divider / Counter (tall)

2×5×3 (30 block volume)
silent, 2-wide stackable (alternating)

output pulse: 2 off-ticks

This version of the circuit trades height and an extra torch to reduce the circuit width to two blocks for closer stacking, but is otherwise identical to the flat version.

Binary Divider reset circuit (top view)

Reset pulse: 3 ticks off or longer

Counter reset circuit which can be added to the binary divider. Parts of the divider circuit are overlaid in lighter color to show positioning; these will be located 2 blocks higher than the reset circuit (see side view).

Binary Divider reset circuit (side view)

Viewed from the side, this shows the location of the torches below the solid blocks of the main divider circuit, and the torch and blocks giving input to the comparator.