Chapter 5

Synchronous Sequential Logic

Introduction:

Sequential circuits employ storage elements in addition to logic gates.

The outputs of a sequential circuit depend on present values of

inputs, and past inputs.

In Bloch diagram the

combinational circuit with memory elements forming a feedback

path.

Categorized/ types of Sequential circuits:

1. Asynchronous:

The storage elements commonly used are time-delay devices.

2. Synchronous:

- has a clock pulse (clocked sequential circuits).

- Use clock pulses to control storage elements are called clocked sequential circuits, - The binary information stored in memory defines the state.

- Flip-flops are storage elements which are used in clocked sequential

circuits.- Each flip-flop can store one bit.

1

(a) Bloch Diagram of A synchronous clocked sequential circuit

Memory/ Storage Elements:

1. Latches:

Storage elements that operate with signal levels. Latches are said

to be level sensitive devices. Latches are the basic types of flip-flop

2. Flip-flops (FF):

It controlled by a clock transition. Flip-flops are edge-sensitive

Type of Latch:

a. SR latch:

The SR latch can be implemented by NOR gates or NAND gates

SR latch- NOR Circuit and Bloch diagram

SR latch- NAND Circuit and Bloch diagram

b. D Latch (Transparent Latch):

Its Cross-coupled SR latch. S and R are never equal to 1 at the

same time.

2

D latch Circuit diagram, Bloch diagram

Trigger:

Trigger: a latch or flip-flop is switched by a change of the control

input

1. Controlled latches are Level triggered

2. Controlled flip-flop is Edge triggered

Flip-flops (FF):

- 1-bit

memory, A sequential circuit may use many flip-flops to store

as many bits as necessary.

- The output of a flip-flop is either 0 or 1 (two states).

Type of Latch:

a. Master–slave/ Edge-Triggered D Flip-flop:

D flip-flop consists of two D latches and an inverter, the first latch is

called the master and the second the slave.

Master–slave Bloch diagram

b. JK Flip-Flop:

Types of flip-flops can be constructed by D flip-flop and external logic

c. T Flip-Flop:

1. Can be obtained from a JK flip-flop with J and K tied together. 2. Can also be constructed with a D flip-flop and an exclusive-OR gate.

T Flip-Flop from a JK flip-flop T Flip-Flop from D flip-flop

3

4

Sate of A sequential circuit

1. Finite State machines (FSMs) models

A sequential circuit has inputs, outputs, and internal states.

Classified/Types of Finite state machine models:

1. The Mealy implementation

2. The Moore implementation

- There are differing only in the way the output is generated.

Moore machine: The outputs of the circuit depend only on the

current state of the circuit.

- Mealy machine: The outputs of the circuit depend on both the

current state of the circuit and the inputs

2. State Equation

Types of analyze a sequential circuit

1. State equations

2. State table

3. State diagram

4. Flip-Flop input equations

Behavior of a clocked Sequential Circuits:

5

This circuit is determined from

1. The inputs

2. The outputs

3. The state of its flip-flops

The behavior of a clocked sequential circuit can be described

algebraically by means of state equations; also called transition

equations.

Example: Two D flip-flops A and B, an input x and output y

Usually, we drop the “(t)”:

3. State Table

6

State table (also called a transition table) enumerates the time

sequence of inputs, outputs, and flip-flop states.

The table consists of four labels: present state, input, next state, and

output.

Note: A sequential circuit with m flip-flops (State) and n inputs need

2m+n rows in the state table.

Second Form of State Table

The state table has three section: present state, next state, and

output

4. State Diagram

The state diagram provides exactly the same information as the state

table and is obtained directly from the state table.

Graphically represent the information in a state table. A state

diagram is a directed graph, where the node (Vertex) represents a

unique state (with its state value inside), and each arc (Edge) a

unique state transition (with inputs/outputs above).

Ex: starting from state 00

7

The binary number inside each circle identifies the state. The

directed lines are labelled with two binary numbers separated by a

slash (/) the input value that causes the state transition is labelled

first. The number after the slash symbol / gives the value of the

output. A directed line connecting a circle with itself indicates that no

change of state occurs..

If the input is 0, it stays at state 00 with output=0

If the input is 1, it goes to state 01 with output=0

State Diagram of Second Form of State Table

5.

5.

5.

5.

5.

5. State Reduction

8

9

6. State Assignment

Assign coded binary values to the states for physical implementation

For a circuit with m states, the codes must contain n bits where 2n≥m

Popular State Assignments:

1. Binary: 2. Gray code: 3. One-hot: 4. Simplify the circuit design but may have larger hardware cost

10