Basic Digital Counter
A digital counter is a sequential logic circuit that counts clock pulses and represents the result in binary form using flip-flops.
Working Principle
- Counts incoming clock pulses
- Stores count in binary form
- Built using flip-flops (T or JK)
4-bit Binary Counter
A 4-bit counter uses 4 flip-flops and can count:
Maximum states: 2⁴ = 16 (0 to 15)
Counting Sequence
| Clock Pulse | Binary Output | Decimal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 15 | 1111 | 15 |
Mathematical Concepts
1. Count Formula
Count = N (number of clock pulses)
2. Modulus
Modulus = 2โฟ
For 4-bit counter: 2⁴ = 16 states
3. Binary Weighting
Bit weights: Q3 Q2 Q1 Q0 = 8, 4, 2, 1
Example:
Binary: 1011
= (1×8) + (0×4) + (1×2) + (1×1)
= 11 (Decimal)
Flip-Flop Operation
- Q0 toggles every clock pulse
- Q1 toggles every 2 pulses
- Q2 toggles every 4 pulses
- Q3 toggles every 8 pulses
Timing Diagram (Concept)
CLK: _|‾|_|‾|_|‾|_|‾|_ Q0 : 0101010101010101 Q1 : 0011001100110011 Q2 : 0000111100001111 Q3 : 0000000011111111
Example Calculation
Clock frequency = 1 kHz
4-bit counter cycles = 16 states
Time per cycle = 16 / 1000 = 0.016 sec
Summary
- Counts clock pulses in binary form
- Uses flip-flops as memory elements
- Maximum count = 2โฟ
- Resets after full cycle (MOD counter)
- Used in timers, CPUs, and digital systems