Sequential Logic

Block diagram of Sequential Circuit

Combinational Circuit

Storage Element

s

Inputs Outpu

tsNext State

Present State

Definition A combinational circuit and storage

elements are interconnected to form sequential circuit.

Storage elements are capable of storing binary information.

It defines the state. Inputs together with the present state of

storage elements determine the output. Determine values used to determine the

next state of storage elements.

Definition ctd… Outputs in a sequential circuit are a function

not only of inputs. Present state of stored elements.

Next state of storage elements is also a function of inputs and present state of stored elements.

Thus, a sequential circuit is specified by a time sequence of inputs, internal states and outputs

Two types

Synchronous Synchronous sequential circuits can be

defined from the knowledge of its signals at discrete instants of time.

Asynchronous Asynchronous sequential circuits

depends upon the inputs at any instant of time and the order in continuous time in which the inputs change.

Synchronous sequential circuits Employs signals that effect storage

elements only at discrete instants of time.

Synchronization is achieved by a timing device called a clock generator.

Clock generator produces a periodic train of clock pulses.

Synchronous sequential circuits use clock pulses as inputs to storage elements are called clocked sequential circuits.

Storage can be constructed from logic with delay connected in a closed loop.

A property - there must be no inversion.

A buffer is usually implemented using two inverters.

Clocked sequential diagrams

Combinational Circuit

Flip-Flops

Inputs Outpu

ts

Clock pulses

Latches

A storage element can maintain a binary state indefinitely, until directed by an input signal to switch states.

Difference between latches and flip-flops No of inputs they possess Manner which the inputs affect the

binary state Most basic storage elements are

latches

S-R Latch

S-R Latch Two cross-coupled NOR gates. Derived from

Replacing inverters with NOR gates.

S-R Latch

Two inputs S - set R – Reset

When Q = 1 and Q’ = 0

Set State Q = 0 and Q’ = 1

Reset State

Outputs Q and Q’ are normally the complements of each other

Function Table

S R Q Q’1 0 1 00 0 1 00 1 0 1

0 0 0 1

1 1 0 0

S’R’ Latch

Two cross-coupled NAND gates.

Function Table

S R Q Q’0 1 1 01 1 1 01 0 0 1

1 1 0 1

0 0 1 1

SR latch with control inputs

Function Table

C S R Next State of Q

0 X X No change1 0 0 No change1 0 1 Q = 0 ; Reset

Time1 1 0 Q = 1 ; Set

State1 1 1 Undefined

Eliminate undesirable undefined state in SR latch is to ensure that inputs S and R are never equal to 1 at the same time.

D Latch

Function Table

C D Next State of Q0 x No change1 0 Q = 0 ; Reset State1 1 Q = 1 ; Set State

Flip-flops

The simplest form of sequential circuit.

Variety of flip flops, all of which share two properties.

One is …. A bistable device. Exists in one of two states In the absence of input, remains in the

state. Thus, can function as a 1 – bit memory.

2nd one Has two outputs. Which are always complements of each

other. Generally labeled Q and Q’.

Flip Flops

Latches are asynchronous, which means that the output changes very soon after the input changes.

Most computers today are synchronous, which means that the outputs of all the sequential circuits change simultaneously to the rhythm of a global clock signal.

A flip-flop is a synchronous version of the latch.

Master-Slave Flip-Flop

There are several fundamental types of flip-flops.

In addition there are minor variations depending on the number of inputs and how they control the state of the flip-flop.

Very simple type of flip-flop called a D-flip-flop.

A master-slave D-flip-flop is built from two SR-latches and some gates

SR Master – Slave Flip-Flop