# Design of a divide by N counter

A divide by N counter counter N number of state following which it resets back to the initial state and starts counting again. For example, a divide by 10 also known as a decade counter counts a total of 10 states from 0 to 9 before resetting to state ‘0’.

For counting up to N states, the number of flip-flops required will be Log_{2} N = Log_{2} 2^{n}

The design steps discussed in binary counters can also be used here. i.e. State diagram, excitation table, simplification of logic equations and then drawing the circuit diagram. Second method in designing these counters could be to use the decoding gates at the output of a binary counter.

**Example-1: Design a divide by 5 counter such that on pressing the switch the count increments**

**Analysis:** On reading the statement, it is clear that the counter will count 5 states from 0 to 4 on every press of a switch.

**Number of flip-flops required:** nearest whole number in the power of 2 is 7, so the number of flip-flops required are: Log_{2} 2^{3 } = 3Log_{2} 2 = 3

The excitation Table: