CS2100: Sequential logic - Circuit Construction

Synchronous Sequential Circuits

A circuit that respond to what is happening.

Examples of circuits:
- Vending machine

- Traffic lights

Key Idea:

- Same input may give different output

- The internal memory elements may affect the result

Memory elements = internal state

- Output is determined by input and output

State Diagram

To use an input/output to change state.

Analyze a sequential circuit

1. Derive its state table (state diagram)

2. Derive state equation for ff inputs AND

3. Derive output functions for the circuit outputs

State table

From the state equation and output function, we derive the state table.

1. Find the equation for each output

2. Derive the state table for each output

3. Compact if necessary by looking at patterns.

Example of State table

State table have up to 2^m+n rows
where m is number of ff and n number of input

Drawing the diagram

1. Draw a state starting from 00 node

2. Draw the transit edge with its input/output

3. Go through each of the row from the state table

m FF have up to 2^m states

With the flip flop input function and the characteristics tables of ff, we obtain the next states of the ff.

FF Naming Convention

JK flip flop:

JA represents the J input for the flip flop A

KA represents the K input for the FF A

FF Excitation Table

Shows the change of state with the use of inputs as reference

It has the same info as the characteristic table except in different order.

Example of JK Excitation convertion

Summary:

Sequential Circuit design

1. Start with circuit specification
 - description of circuit behavior (state diagram/state table)
 - Derive state table

 - Perform state reduction/Assignment if needed

2. Determine number of FF and label

- 2 bits = 2 ff

3. Choose the type of FF to be use

4. Derive circuit excitation and output function from state table

JK/SR: Look as the excitation table

D: Just copy directly from state change

Note: For SR there are some combination that are missing due to the invalid input/output

5. Derive circuit output functions and ff input function

- Use kmap

6. Draw logic diagram