Sequential Circuit - Design
Tags: #◇Computer Science #◇CSARCH1 #◇Problem Solving #◇M5
◇Overview
The process of designing a synchronous sequential circuit goes from a high-level word description down to the logic diagram.
Design Procedure
- From the word description, derive a state diagram for the circuit.
- Reduce the number of states if necessary.
- Assign binary values to the states.
- Obtain the binary-coded state table.
- Choose the type of flip-flops to be used.
- Derive the simplified flip-flop input equations and output equations (using K-maps and Excitation Tables).
- Draw the logic diagram.
Workflow: Word problem -> State Diagram -> State Table -> Excitation Table -> Equations -> Circuit.
◇Important Formulas: Excitation Tables
Excitation tables specify what inputs are required at the flip-flops to cause a desired state transition from Q(t) to Q(t+1).
D Flip-Flop:
| Q(t) | Q(t+1) | D |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
T Flip-Flop:
| Q(t) | Q(t+1) | T |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
JK Flip-Flop:
| Q(t) | Q(t+1) | J | K |
|---|---|---|---|
| 0 | 0 | 0 | X |
| 0 | 1 | 1 | X |
| 1 | 0 | X | 1 |
| 1 | 1 | X | 0 |
SR Flip-Flop:
| Q(t) | Q(t+1) | S | R |
|---|---|---|---|
| 0 | 0 | 0 | X |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | X | 0 |
◇Worked Examples
Example: Sequence Detector (Consecutive 1s)
Design a circuit that detects a sequence of three or more consecutive 1’s in a string of bits. Output is 1 when there are 3 or more 1s. Use D flip-flops.
- State Assignment:
S0 = 00,S1 = 01,S2 = 10,S3 = 11 - Use the D Flip-flop Excitation Table to determine inputs
DAandDBrequired for state transitions. - Simplify logic using Karnaugh maps for
DA,DB, andY. - Draw the circuit logic diagram using basic gates and D Flip-Flops.
Example: 3-bit Binary Counter
Design a 3-bit binary counter using T flip-flops.
- Since it counts from 0 to 7 (000 to 111), it requires 3 T flip-flops (
A2,A1,A0). - Use the T Flip-flop Excitation Table to determine inputs
TA2,TA1, andTA0. - Generate K-maps and find input formulas.
- Draw the circuit logic diagram.
◇References & Navigation
- Previous Topic: ◇Sequential Circuit - State reduction and assignment
- Next Topic: ◇Hardware Description Language for sequential circuit
- Related Notes: ◇Sequential Circuit - State reduction and assignment
ACTIVE RECALL VERIFICATION
Select an answer to verify conceptual comprehension and reveal the technical rationale.
What is typically the first step in the design procedure for a synchronous sequential circuit?
After obtaining the state diagram, what is often the next step to optimize the design?
What tool is heavily used to find the simplified flip-flop input equations from the excitation table?
What is the purpose of an excitation table in sequential circuit design?
In an excitation table for a D flip-flop, what must the input D be to transition from Q(t)=0 to Q(t+1)=1?
In an excitation table for a JK flip-flop, if Q(t)=0 and Q(t+1)=0, what are the values of J and K?
For a T flip-flop, what must the input T be to maintain the current state (Q(t) to Q(t+1) is 1 to 1)?
When designing a 3-bit binary counter, how many flip-flops are required?
What is the sequence of steps for sequential design?
During state assignment, what is done?