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1. State Diagram Creation:
The first step is to represent the desired sequence visually using a state diagram. Each state in the diagram represents a specific count value (0, 2, 3, 5, 6).
Draw circles for each state and label them with the corresponding count value.
visually representing the desired sequence directed arrows to show transitions between states. Annotate each arrow with the input that causes the transition (usually a clock pulse).
2. State Transition Table Derivation:
From the state diagram, create a state transition table. This table lists the current state, the next state it transitions to on a clock pulse, and (optionally) any additional inputs that might influence the transition.
3. Next State Logic Determination:
Analyse the state transition table and determine the logic required for each flip-flop's next state based on the current state. This will involve using combinational logic gates (AND, OR, NAND, etc.) to generate the appropriate control signals for the flip-flops.
4. Flip-Flop Selection and Circuit Design:
Choose the type of flip-flops (D flip-flops, JK flip-flops, etc.) based on the complexity of the next state logic.
Implement the combinational logic using logic gates to generate the control signals for the flip-flops as determined in step 3.
Connect the clock signal, control signals from the logic gates, and flip-flop outputs according to the designed logic.
Example: Counter for Sequence 0, 2, 3, 5, 6, 0
Sol: - Step 1. State Diagram:
Step 2. State Transition Table:
Current State | Next State | CLK |
0 | 2 | + |
2 | 3 | + |
3 | 5 | + |
5 | 6 | + |
6 | 0 | + |
Step 3. Next State Logic:
To go from 0 to 2, we need the output of the flip-flop representing the current state (let's call it Q0) to be 0.
To go from 2 to 3, Q0 should be 1.
Similarly, for transitions from 3 to 5 and 5 to 6, Q0 should alternate between 0 and 1.
To return from 6 to 0, we need Q0 to be 1.
Step 4. Circuit Design with D Flip-Flops:
We can use two D flip-flops (D0 and D1) for this counter.
The logic for the D inputs can be derived from the next state logic analysis:
D0 = Q0' (inverts the current state)
D1 = Q0 (copies the current state)
Connect the clock signal, D0, and D1 to the respective inputs of D0 and D1.
The output of D1 (representing the current state) can be used as the count output of the counter.
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