Chapter 1: Q39E (page 2)
Question: Construct a 3-bit counter using three D flip-flops and a selection of gates. The inputs should consist of a signal that resets the counter to 0, called reset, and a signal to increment the counter, called inc. The outputs should be the value of the counter. When the counter has value 7 and is incremented, it should wrap around and become 0.
Short Answer
Answer
The 3-bit counter using D flip-flops:
Step by step solution
Truth table for 3-bit counter
The truth table for 3-bit counter is given below:
Current State | Next State | Output | ||||||
I2 | I1 | I0 | I2 | I1 | I0 | C | B | A |
0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Logic equations for 3-bit counter
The logic equations for next state are:
C = I2’.I1.I0 + I2.I1’+I2 or I0I1’+I0I2’+I0’I2
B = I1 XOR I2
A = I0’
For reset input, the final input of the flip flop is:
C = I2 . R’
B = I1 . R’
A = I0 . R’
For increment inc input, the counter is incremented:
c_out = inc . c_in
Design 3-bit counter using D flip-flops
The 3-bit counter using D flip-flops:
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