# Digital Counters - Computer Logical Organization

## What are Digital Counters?

The counter which is a digital circuit which facilitates in pulses counting. One of the widest applications of flip-flops is Counter. There are two types of counters -

• Asynchronous or ripple counters.
• Synchronous counters.

## Asynchronous or ripple counters

The 2-bit ripple up counter uses toggle (T) flip flop. Ripple counters use JK flip-flop toggle., where J and K are permanently connected to logic 1. To the internal clock input of flip flop A, external clock QA is applied. The output of the previous clock is applied to the clock input of the next flip-flop, FF-B.

### Logical Diagram ### Operation

 S.N. Condition Operation 1 Initially let both the FFs be in the reset state Initially QBQA= 00 2 After 1st negative clock edge When the first negative edge is applied, QA is equal to 1 and FF-A will toggle. QBQA= 01 after the first clock pulse. 3 After 2nd negative clock edge For the second negative clock edge, QA= 0 and FF-A toggles. After the second clock pulse, QBQA= 10. 4 After 3rd negative clock edge On the arrival of 3rd negative clock edge, FF-A toggles again and QAbecome 1 from 0. QBQA= 11 after the third clock pulse. 5 After 4th negative clock edge On the arrival of 4th negative clock edge, FF-A toggles again and QAbecomes 1 from 0. This negative change in QAacts as clock pulse for FF-B. Hence it toggles to change QBfrom 1 to 0. QBQA= 00 after the fourth clock pulse.

### Truth Table ## Synchronous counters

In Synchronous counters, the clock pulses are applied to all the flip-flops simultaneously.

### 2-bit Synchronous up counter

Here two inputs of FF-A, JA and KA are tied to logic 1 and FF-A work as toggle flip-flop. The inputs JB and KB inputs are connected to QA.

Logical Diagram Operation

 S.N. Condition Operation 1 Initially let both the FFs be in the reset state Initially, QBQA= 00 . 2 After 1st negative clock edge FF-A will toggle when first negative clock edge is applied and QA change from 0 to 1. After the first clock pulse, QBQA= 01. 3 After 2nd negative clock edge FF-A toggles again and QAchanges from 1 to 0. After the second clock pulse, QBQA= 10. 4 After 3rd negative clock edge After the third clock pulse, QBQA= 11. 5 After 4th negative clock edge After the fourth clock pulse, QBQA= 00.

## What are different types of counters?

The synchronous or asynchronous counters are classified into:

• 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

All the FFs operate in toggle mode in UP/DOWN ripple counter by using T flip-flops or JK flip-flops. The clock is directly received by the LSB flip – flop. But for every other FF, the clock is obtained from the output of the previous FF, (Q = Q bar).

• UP counting mode (M=0) – To the clock of the next stage, Q output of the preceding FF is connected. At logic 0, the mode select input M is situated.
• 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.

• FFs are essential as it is 3-bit.
• A mode control input is required.
• For the clock input of the next one, Q output of preceding FF is connected.
• The mode control input M controls the preceding FF by Q and Q bar output in case of M = 0, UP counting and vice versa.

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 disabled gates are AND 2 and 4 and enabled gates are AND 2 and 4. To the clock input of FF-B, QAgets connected. To the clock input of FF-C, QB gets connected. 2 Case 2: With M = 1 (Down counting mode) If M = 1, then the disabled gates are AND 1 and 3 and enabled gates are AND 2 and 4. To the clock input of FF-B, QAgets connected. To the clock input of FF-C, QB gets connected.

## What is Modulus Counter (MOD-N Counter)?

MOD-4 counter is 2-bit ripple counter and MOD-8 is 3-bit ripple counter. Therefore a modular – N counter is an n-bit ripple counter bearing the MOD number as 2n.

Type of modulus

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

## What are the different applications of counters?

Counters are applied in the following areas:

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

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