Synchronous MOD-5 counter; counter applications

Synchronous MOD-5 counter

A MOD-5 counter has 5 states, 000 → 001 → 010 → 011 → 100 → 000. Three JK flip-flops ($2^3 = 8 \ge 5$) share a common clock. States 101, 110, 111 are don't cares.

Excitation table (JK: 0→0: 0X, 0→1: 1X, 1→0: X1, 1→1: X0)

K-maps

The other maps give $K_0 = 1$, $J_1 = K_1 = Q_0$ and $K_2 = 1$.

Equations

$$\begin{aligned} &J_2 = Q_1Q_0,\quad K_2 = 1 \\ &J_1 = Q_0,\quad K_1 = Q_0 \\ &J_0 = \overline{Q_2},\quad K_0 = 1 \end{aligned}$$

Block (circuit) diagram

   +-----+       +-----+       +-----+
J0>|J   Q|-Q0 J1>|J   Q|-Q1 J2>|J   Q|-Q2
   | FF0 |       | FF1 |       | FF2 |
K0>|K    |    K1>|K    |    K2>|K    |
   +--o--+       +--o--+       +--o--+
      |             |             |
CLK---+-------------+-------------+
J0 = Q2'   K0 = 1
J1 = Q0    K1 = Q0
J2 = Q1.Q0 K2 = 1

Unused states: 101 → 010, 110 → 010, 111 → 000, so the counter is self-starting.

Timing diagram

CLK  __|‾|_|‾|_|‾|_|‾|_|‾|_|‾|_|‾|_|‾
Q2   ________________|‾‾‾|___________
Q1   ________|‾‾‾‾‾‾‾|___________|‾‾‾
Q0   ____|‾‾‾|___|‾‾‾|_______|‾‾‾|___
Cnt  0    1   2   3   4   0   1   2

$Q_2$ is high for one clock period out of five, so it divides the clock frequency by 5.

Applications of counters

• Frequency division (divide-by-N), e.g. getting 1 Hz from 50 Hz in clocks.
• Digital clocks, watches and timers.
• Counting events or objects (production lines, people counters).
• Frequency counters and digital meters.
• Counter-type (digital-ramp) and dual-slope ADCs.
• Program counter and address generation in computers.
• Generating control sequences and timing signals.

Applications of shift registers

• Serial-to-parallel and parallel-to-serial data conversion (UART, serial communication).
• Temporary data storage and time delay.
• Ring and Johnson counters, sequence generators.
• Multiplication and division by 2 (shift left / right).
• Pseudo-random sequence generation (LFSR) and error checking (CRC).
• Keyboard scanning and display multiplexing.