Sequential Circuit - Analysis
Tags: #◇Computer Science #◇CSARCH1 #◇Problem Solving #◇M5
◇Overview
Analysis of a synchronous sequential circuit entails determining its behavior from a given logic circuit, moving ultimately to its state diagram.
The maximum number of values an n-bit memory can store is 2^n. This is also the maximum number of states a sequential circuit with n flip-flops can have.
Steps to analyze:
- Solve for flip-flop input equations (if not given).
- Create the state transition table.
- Draw the state transition diagram.
◇Finite State Machines
Mealy Finite State Machine
- Output is a function of both the present state and the input.
- The state diagram shows both input and output values along the directed lines (e.g.,
input/output). - Outputs may change if inputs change during the clock cycle.
- May produce momentary false values (glitches) due to combinational delays before the active clock edge.
Moore Finite State Machine
- Output is a function of only the present state.
- The state diagram usually shows the outputs inside the circles along with the state name. The directed lines only show the inputs.
- Outputs are strictly synchronized with the clock.
◇Important Formulas
Flip-Flop Characteristic Tables
D Flip-Flop:
| D | Q(t+1) |
|---|---|
| 0 | 0 |
| 1 | 1 |
T Flip-Flop:
| T | Q(t+1) |
|---|---|
| 0 | Q(t) |
| 1 | Q'(t) |
JK Flip-Flop:
| J | K | Q(t+1) |
|---|---|---|
| 0 | 0 | Q(t) |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | Q'(t) |
SR Flip-Flop:
| S | R | Q(t+1) |
|---|---|---|
| 0 | 0 | Q(t) |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | Indeterminate |
◇Worked Examples
Example 1: D Flip-Flop Analysis
Given 2 D Flip-Flops (A, B); input: x, output: y.
Input equations:
DA = Ax + BxDB = A'xy = (A+B)x' = Ax' + Bx'
Derive the State Table by evaluating DA and DB for every combination of A, B, and x, which gives the next states A(t+1) and B(t+1).
Example 2: JK Flip-Flop Analysis
Given 2 JK Flip-Flops (A, B); input: x.
Input equations:
JA = BKA = Bx'JB = x'KB = A ⊕ x = Ax' + A'x
Determine next states using the JK characteristic table.
Example 3: T Flip-Flop Analysis
Given 2 T Flip-Flops (A, B); input: x, output: y.
Input equations:
TA = BxTB = xy = AB
Determine next states using the T characteristic table. (This represents a Moore Machine where output y depends only on states A and B).
◇References & Navigation
- Previous Topic: ◇Introduction to Sequential Circuit
- Next Topic: ◇Sequential Circuit - State reduction and assignment
- Related Notes: ◇Introduction to Sequential Circuit, ◇Sequential Circuit - Design
ACTIVE RECALL VERIFICATION
Select an answer to verify conceptual comprehension and reveal the technical rationale.
What is the maximum number of states a sequential circuit with n flip-flops can have?
What is the first step in analyzing a synchronous sequential circuit if the flip-flop input equations are not given?
What distinguishes a Mealy Finite State Machine from a Moore FSM?
In a Moore Finite State Machine, the output depends entirely on:
Where are outputs typically indicated in the state diagram of a Mealy machine?
In a Moore machine's state diagram, where are the outputs typically shown?
Why might the output of a Mealy machine have momentary false values (glitches)?
When analyzing a circuit with JK flip-flops, what is needed to determine the next state from the present state and inputs?
What is the characteristic equation for a T flip-flop?
Which of the following equations accurately represents a D flip-flop's behavior?