Lecture 2 - Combinational and Sequential Logic

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1Digital Electronics EEE3017WR. Verrinder (2008)

Announcements

Laboratories and Tutorials will be held at the following times:

Monday (15h00 17h00)

Tuesday (15h00 17h00)

Venue Change: Laboratory 1 will be held in the White Lab

Tutorials will be handed out during the tut session and must be

completed and handed in by your next lecture (Thursday Lectures)

It is a DP requirement to attend at least 50% of all labs and tutorials


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Textbooks

There is no set textbook for this course, however, these

books maybe useful for certain sections of work:

Logic and Computer Fundamentals (Mano & Kine)

The Art of Electronics (Horowitz & Hill)


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Digital Circuits

There are two main

classes of digital

circuits:

Combinational Circuits

Sequential Circuits


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Combinational Circuits

Have no memory

Output only depends on the inputs

To reverse engineer the circuit:

Cycle through all the inputs and note the outputs for

each input

INPUT OUTPUT1 2 3


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Sequential Circuits

Have memory

Output is a function of inputs and the state of

the circuit

Cannot just use inputs and outputs to determinethe circuits construction

OUTPUTINPUT


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Off the Shelf Digital Chips

Some digital functions

are so useful that they

have dedicated chips

This include: Multiplexers

Decoders

Adders

Flip-flops

Counters etc.


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Multiplexers

Are selector devices Take multiple inputs and

output one signal based on

the value of the select

signals

Have:

n inputs

1 output log2n selection lines

Examples: 74HC157; 74HC153;

74HC356

Sel1 Sel2 Output

0 0 In0

0 1 In1

1 0 In2

1 1 In3


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Multiplexers cont.


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Encoder

Converts a signal into

a specific code

Used for:

Encrypting data

Data compression

Translating one code

to another

In3 In2 In1 In0 Out1 Out0

0 0 0 1 0 00 0 1 0 0 1

0 1 0 0 1 0

1 0 0 0 1 1


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Addition Circuits Half Adder

Adds 2 bits together

A

+ BSum

Sum: AB Carry: A.B

Problem!

0

001

0

1

1

1Carry1

1

0


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Problem!

Adds two bits together but cant handle an

input carry bit

This is why it is called a half adder

SolutionFULL ADDER


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Addition Circuits Full Adder

Has 3 inputs:

Input A

Input B

Carry In

2 outputs

Sum

Carry Out

Made by combining 2 half

adders and an OR gate


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Multi-bit Wide Adder

To make multi-bit wide adders:

Cascade a number of full adders

The carry out bits are fed into the carry in bits

etc.

Problems with this approach:

Cascading circuits leads to poor overall circuit

performance

Chips not infinitely fast


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RS Flip-flops

Have memory

Made by cross-coupling

two:

NAND gates

NOR gates

Pull LOW and Q goes

HIGH and stays HIGH

until pulled LOW

S

R


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D-type Flip-Flops

Have following inputs: D Clock (CLK)

S

R

Have following outputs Q Q

On clock edge, the value

on D is transferred to Qand stays there

R and S are used to putdevice into known state

D CLK Next State of Q

X 0 No Change

0 h 01 h 1


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JK Flip-flops

Operation similar to D-type except has twoinputs J and K

When J is HIGH, flip-flopis SET

When K is HIGH, flip-flopis RESET

If both J and K are high,output simply TOGGLES

J K Next State of Q

0 0 No change

0 1 0

1 0 1

1 1 Toggle


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Counters

Go through a set sequence of states when pulsesare applied to the input

Different types:

Ripple counters

Synchronous counters

Johnson counters

Decade counters.

Up-down counters Ring counters


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Ripple Counter

Made using flip-flops which can complement their

outputs

2nd flip-flop only toggles when first flip-flop has changed

state

Outputs do not all change at the same time


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Shift Registers

Data is put in load input

For every clock pulse, data is shifted 1 bit to the right

Used to implement: Parallel to serial conversion

Used often in microprocessors

Serial to parallel conversion

101

10 0 01 1


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Design of Sequential Circuits

using D-type Flip-flops D-type flip-flops used to hold systems current state

Use combinational logic to make system move from

state to state

Flip flops holdCURRENT

state

Combinational

circuit calculates

NEXTstate

Combinational

logic calculates

OUTPUTS for

each state

D inputs

System

Inputs

Q

Outputs SystemOutputs


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How to Design the

Combinational Circuit

Draw a present state

next state diagram

Show:

Inputs

Present States

Next States

Enter values in next

state column given

inputs and current state

Simplify using standard

logic reduction tools

Input

Present

1

(Q1)

Present

0

(Q0)

Next

1

(D1)

Next

0

(D0)

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1


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Example 1 - Solution

Firstly there are no external inputs

Use two D-type flip flops as

This gives us 4 possible states. This is fine as we just use dont care

conditions for the unwanted state

To create the combinational logic use aPresent state Next State Diagram


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Example 1 Solution cont.

Present Next

(Q1) (Q0) (D1) (D0)

0 0

0 1

1 0

1 1

D1 = Q0 Need to use a

Karnaugh Map to

find D00 0

0 1

01

X X

Count Sequence:

0-1-2-repeat


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Example 1 Solution cont.

)QQ(

QQD

10

100

0 1

0

1

Q0

Q1

1

X


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Documents

Lecture 2 - Combinational and Sequential Logic