# Digital Counters

Counter is a sequential circuit. A digital circuit which is used for a counting pulses is known counter. Counter is the widest application of flip-flops. It is a group of flip-flops with a clock signal applied. Counters are of two types.

- Asynchronous or ripple counters.
- Synchronous counters.

## Asynchronous or ripple counters

The logic diagram of a 2-bit ripple up counter is shown in figure. The toggle (T) flip-flop are being used. But we can use the JK flip-flop also with J and K connected permanently to logic 1. External clock is applied to the clock input of flip-flop A and Q_{A} output is applied to the clock input of the next flip-flop i.e. FF-B.

### Logical Diagram

### Operation

S.N. | Condition | Operation |
---|---|---|

1 | Initially let both the FFs be in the reset state |
Q_{B}Q_{A} = 00 initially |

2 | After 1st negative clock edge |
As soon as the first negative clock edge is applied, FF-A will toggle and Q Q Q |

3 | After 2nd negative clock edge |
On the arrival of second negative clock edge, FF-A toggles again and Q The change in Q Q |

4 | After 3rd negative clock edge |
On the arrival of 3rd negative clock edge, FF-A toggles again and Q Since this is a positive going change, FF-B does not respond to it and remains inactive. So Q Q |

5 | After 4th negative clock edge |
On the arrival of 4th negative clock edge, FF-A toggles again and Q This negative change in Q Q |

### Truth Table

## Synchronous counters

If the "clock" pulses are applied to all the flip-flops in a counter simultaneously, then such a counter is called as synchronous counter.

### 2-bit Synchronous up counter

The J_{A} and K_{A} inputs of FF-A are tied to logic 1. So FF-A will work as a toggle flip-flop. The J_{B} and K_{B} inputs are connected to Q_{A}.

### Logical Diagram

### Operation

S.N. | Condition | Operation |
---|---|---|

1 | Initially let both the FFs be in the reset state |
Q_{B}Q_{A} = 00 initially. |

2 | After 1st negative clock edge |
As soon as the first negative clock edge is applied, FF-A will toggle and Q But at the instant of application of negative clock edge, Q Q |

3 | After 2nd negative clock edge |
On the arrival of second negative clock edge, FF-A toggles again and Q But at this instant Q Q |

4 | After 3rd negative clock edge |
On application of the third falling clock edge, FF-A will toggle from 0 to 1 but there is no change of state for FF-B. Q |

5 | After 4th negative clock edge |
On application of the next clock pulse, Q Q |

## Classification of counters

Depending on the way in which the counting progresses, the synchronous or asynchronous counters are classified as follows −

- Up counters
- Down counters
- Up/Down counters

## UP/DOWN Counter

Up counter and down counter is combined together to obtain an UP/DOWN counter. A mode control (M) input is also provided to select either up or down mode. A combinational circuit is required to be designed and used between each pair of flip-flop in order to achieve the up/down operation.

- Type of up/down counters
- UP/DOWN ripple counters
- UP/DOWN synchronous counter

## UP/DOWN Ripple Counters

In the UP/DOWN ripple counter all the FFs operate in the toggle mode. So either T flip-flops or JK flip-flops are to be used. The LSB flip-flop receives clock directly. But the clock to every other FF is obtained from (Q = Q bar) output of the previous FF.

**UP counting mode (M=0)**− The Q output of the preceding FF is connected to the clock of the next stage if up counting is to be achieved. For this mode, the mode select input M is at logic 0 (M=0).**DOWN counting mode (M=1)**− If M = 1, then the Q bar output of the preceding FF is connected to the next FF. This will operate the counter in the counting mode.

### Example

3-bit binary up/down ripple counter.

3-bit − hence three FFs are required.

UP/DOWN − So a mode control input is essential.

For a ripple up counter, the Q output of preceding FF is connected to the clock input of the next one.

For a ripple up counter, the Q output of preceding FF is connected to the clock input of the next one.

For a ripple down counter, the Q bar output of preceding FF is connected to the clock input of the next one.

Let the selection of Q and Q bar output of the preceding FF be controlled by the mode control input M such that, If M = 0, UP counting. So connect Q to CLK. If M = 1, DOWN counting. So connect Q bar to CLK.

### Block Diagram

### Truth Table

### Operation

S.N. | Condition | Operation |
---|---|---|

1 | Case 1 − With M = 0 (Up counting mode) |
If M = 0 and M bar = 1, then the AND gates 1 and 3 in fig. will be enabled whereas the AND gates 2 and 4 will be disabled. Hence Q These connections are same as those for the normal up counter. Thus with M = 0 the circuit work as an up counter. |

2 | Case 2: With M = 1 (Down counting mode) |
If M = 1, then AND gates 2 and 4 in fig. are enabled whereas the AND gates 1 and 3 are disabled. Hence Q These connections will produce a down counter. Thus with M = 1 the circuit works as a down counter. |

## Modulus Counter (MOD-N Counter)

The 2-bit ripple counter is called as MOD-4 counter and 3-bit ripple counter is called as MOD-8 counter. So in general, an n-bit ripple counter is called as modulo-N counter. Where, MOD number = 2^{n}.

### Type of modulus

- 2-bit up or down (MOD-4)
- 3-bit up or down (MOD-8)
- 4-bit up or down (MOD-16)

## Application of counters

- Frequency counters
- Digital clock
- Time measurement
- A to D converter
- Frequency divider circuits
- Digital triangular wave generator.