Sequential Logic

There are 2 types of sequential circuits:

• Synchronous: outputs change at specific time
• Asynchronous: Changes at any time

Multivibrator

Class of sequential circuits

• Bistable (2 stable states)
• Monostable or one-shot (1 stable state)
• Astable (no stable state)

Bistable logic devices

Latches, and flip flops.

Memory Elements

Memory element

A device which can remember value indefinitely, or change value on command from its inputs.

Latch

S-R Latch

S-R Latch

Two inputs: S and R Two complementary outputs: Q and Q'

State Q = HIGH: SET Q' = LOW: RESET

				LOW
				initial
				HIGH
				HIGH
				invalid

Active-Low S-R Latch

NAND gates are used instead for this. For these latches, given the input SR:

• 00 becomes an invalid command (no change in Active-High)
• 11 becomes a nochange command (invalid in Active-High)
• 01 becomes a set command (reset in Active-High)
• 10 becomes a reset command (set in Active-High)

Gated S-R Latch

Gated S-R Latch

S-R latch + enable input (EN) and 2 NAND gates

Gated D Latch

With the gated `D` latch, the invalid condition is eliminated.

Flip-Flops

Synchronous bistable devices

Output changes state as a specified point on a triggering input called the clock:

S-R flip flop

				No change
				Reset
				Set
				Invalid

D flip flop

			Set
			Reset

J-K flip flop

				No change
				Reset
				Set
				Toggle

T flip flop

			No change
			Toggle

Asynchronous Inputs

The S-R, D, J-K inputs are synchronous inputs as data on these inputs are transferred to the flip-flop’s output only on the triggered edge of the clock pulse.

Asynchronous

Affect the state of the flip flop independent of the clock

PRE = HIGH: Q is immediately set to HIGH

CLR = HIGH: Q is immediately cleared to LOW

Flip-flop in normal operation mode when both PRE and CLR are LOW.

Synchronous Sequential Circuits

Note

Flip flops make up the memory while the gates form one or more combinational sub-circuits.

				No change
				Reset
				Set
				Invalid/Unpredictable

			Set
			Reset

				No change
				Reset
				Set
				Toggle

			No change
			Toggle

Analysis of Sequential Circuits

Analysing behaviour

1. Derive state table
2. and hence its state diagram

Requires state equations to be derived for the flip-flop inputs as well as output functions for the circuit outputs other than the flip-flops other than flip flops.

or and or can represent the present state and next state of a flip-flop represented by .

State table

Similar to a truth table. Inputs and present state on left side. Outputs and next state on the right side.

flip-flops and inputs rows

Present StateNext StateInputOutputABxAB++ym flip flopsn inputsrowsPresent StateNext StateA BA B++FULL TABLEAB++x=0x=1Outputyyx=0x=1COMPACT TABLE

State diagram

• Each state is denoted by a circle
• Each arrow denotes a transition of the sequential circuit

Circuit output functions

The outputs of a sequential circuit are functions of the present states of the flip-flops and the inputs. The algebraic description of these are the circuit output functions.

Flip-flop input functions/equations

Algebraic descriptions of the part of the circuit that generates inputs to the flip-flops.

This determines the next state generation - using the functions and the characteristic tables, the next states of flip-flops can be obtained.

Flip-flop Excitation Tables

Analysis

Starting from a circuit diagram, derive state table or state diagram

Characteristic tables

Design

Starting from a set of specifications (in the form of state equations, state table, state diagram), derive logic circuit.

Excitation tables

Excitation tables

Input: Required transition from present state to next state Output: Flip-flop inputs

Design procedure:

• Circuit specifications
  • Description of circuit behaviour - state diagram/state table
• Derive state table
• Perform state reduction if necessary
• Perform state assignment
• Determine number of flip-flops and label them
• Choose type of flip-flop to be used
• Derive circuit excitation and output tables from the state table
• Derive circuit output functions and flip-flop input functions
• Draw the logic diagram

Worked example:

> [!question] How many flip-flops are needed? > > Since two bits are needed to represent each state, two flip-flops are needed. > > The flip-flops can be allocated as `A` and `B`.

How many input variables are there?

The input variables are only 0 and 1, meaning there is one input variable.

The input variable can be allocated x.

Present State	at	at
00	00	01
01	10	01
10	10	11
11	11	00

Using JK Flip-flop excitation table

0	0	0	X
0	1	1	X
1	0	X	1
1	1	X	0

We can get the state table:

00	0	00	0	X	0	X
00	1	01	0	X	1	X
01	0	10	1	X	X	1
01	1	01	0	X	X	0
10	0	10	X	0	0	X
10	1	11	X	0	1	X
11	0	11	X	0	X	0
11	1	00	X	1	X	1

X00X00X0X0X1XABxX0X0X1XABx0011XXXABxXXX11ABx # Sink State

Sink state

A state that never moved out of itself to other states