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Modern DigitalModern Digital ElectronicsElectronics

Lectureter : Xie Songyun

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Chapter6:Combinational Logic Design Using MSI Circuits

combinational logic circuits sequential logic circuits function table full adder decoder encoder multiplexer demultiplexer Digital Comparator parity Generator/Checker middle scaled integrated circuits (MSI) common encoder priority encoder8-3 Octal-to-Binary encoder- decimal-to- BCD encoder active-high active-low

extend end complement code

Glossary

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Chapter6:Combinational Logic Design Using MSI Circuits

6.1 IntroductionUsing the methods of combinational circuit designUsing the methods of combinational circuit design

which have been discussed in Chapter 5, complexwhich have been discussed in Chapter 5, complex

functions have been integrated (MSI) and are easilyfunctions have been integrated (MSI) and are easilyavailable in IC form. There is an attractive array ofavailable in IC form. There is an attractive array of

devices such asdevices such as encoders, decoders, adders,

multiplexers, demultiplexers, Parity generators/checkers,

comparators, etc.

Advantages:

Reduce IC package count thereby reducing the system cost.

The system design is greatly simplified because the laborious and

time consuming simplification methods are generally not required.

Improve the reliability of the system by reducing the number of

external wired connections.

Requirement Familiar with the function performed, the

options available, and the limitations of

these devices.

Make an effective and optimum use of MSI

to design a more complex digital circuits .

Requirement Familiar with the function performed, the

options available, and the limitations of

these devices.

Make an effective and optimum use of MSI

to design a more complex digital circuits .

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What is encode? The process of using textdigits or

symbols to represent the special object is called encode.

EX: the number of athlete XXXX represents an athlete.One-bit decimal 0~9, altogether 10 codes.

Two-bit decimal 00~99, altogether 100 codes.

Three-bit decimal 000~999, altogether 1000 codes. In the digital system: for 2n general information,there are n-bit binary number of codes.

What is encoder

A circuit which can perform the function of encoding

The logic symbol of encoder: X: general information

Ycodes

6.2 Encoder and Priority Encoders

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Two types of encoders: common encoderpriority encoder.

In a common encoder, only one encode signal is allowed at any time,it is not allowed to input many encode signals simultaneously.

(1)The Truth table

Octal-to

-Binary

Enc

oder

0I

1I

7I

0Y

1Y

2Yinput output

I0 I1 I2 I3 I4 I5 I6 I7 Y2 Y1 Y0

1 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 1

0 0 1 0 0 0 0 0 0 1 0

0 0 0 1 0 0 0 0 0 1 1

0 0 0 0 1 0 0 0 1 0 0

0 0 0 0 0 1 0 0 1 0 1

0 0 0 0 0 0 1 0 1 1 0

0 0 0 0 0 0 0 1 1 1 1

Octal-to-binary encoder,the input is 8 signals I0-I7(active-high), and the

output is 3 bit binary code

Y2Y1Y0 (active-high).

Ex1: How to design a Octal-to-binary encoder

6.2.1 Common Encoder

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(2) Obtain the logic expression.

input output

I0 I1 I2 I3 I4 I5 I6 I7 Y2 Y1 Y0

1 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 1

0 0 1 0 0 0 0 0 0 1 0

0 0 0 1 0 0 0 0 0 1 1

0 0 0 0 1 0 0 0 1 0 00 0 0 0 0 1 0 0 1 0 1

0 0 0 0 0 0 1 0 1 1 0

0 0 0 0 0 0 0 1 1 1 1

76542 IIIIY

76321 IIIIY

75310 IIIIY

Realize the encoding circuit with 3 ORgates according to the output expression.

1

1

1

Y2

Y1

Y0

I7I6I5I4I3I2I1

6.2.1 Common Encoder

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input output

I0 I1 I2 I3 I4 I

5

I6 I7 Y2

Y1

Y0

1 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 1

0 0 1 0 0 0 0 0 0 1 0

0 0 0 1 0 0 0 0 0 1 1

0 0 0 0 1 0 0 0 1 0 0

0 0 0 0 0 1 0 0 1 0 1

0 0 0 0 0 0 1 0 1 1 0

0 0 0 0 0 0 0 1 1 1 1

76542 IIIIY

Since the input signals repel

each other, so 0II mn

I nI m encoded objectUnencoded object

II

IIIIIIIII

IIIIIIIIIIIIIIII

I

44

765321044

765321044

76532104

Take out one term to analyze:IIIIIIIIIIIIIIII

IIIIIIIIY

65432107

76432105

765321042

so

thus76321 IIIIY

75310 IIIIY

How to simplified the logic expression.6.2.1 Common Encoder

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I0 I1 I2 I3 I4 I5 I6 I7 I8 I9

0 0 0 00 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

0 1 0 10 1 1 0

0 1 1 1

1 0 0 0

1 0 0 1

A3A2A1A0

One of the most commonly used input device for a digital system isa set of ten switches, one for each numeral between 0 and 9.

1 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 1

inputs outputsfeature:

Only one channel is allowed to input 1,

the others input 0 at any time.

The output is encode to the input 1

0000 represents encode to I0.

0001represents encode to I1.

1001 represents encode to I9.

A3=I8+I9A2=I4+I5+I6+I7

A1=I2+I3+I6+I7A0=I1+I3+I5+I7+I9

8I 9I I4~I7I2I3I6I7 I1I3I5I7I9

EX2: Design a decimal-to-BCD Encoder

A3 A2 A1 A0

6.2.1 Common Encoder

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0)( STSif All the gate circuits open

STIIIIY )( 76542

STIIIIIIIIY )( 765435421

STIIIIIIIIIIY )( 76564354210

To extend the circuit function and

increase the flexibility of usage, MSI circuit74LS148, the control circuit is composed of

gates G1G2 and G3.

)(STS select input ends

1)( STS

The encoder works in

normal state.

All the output ends are

locked at high level.

0)( STS&

&

&

&

&

I1

I2

I0

I3

I4

I5

I6

I7

S

YS

YEX

Y0

Y1

Y2

1

1

1

1

1 1

1

1 1

1 1

1 1

1

1(ST)

G1

G2

G3

0 1

0)( STS

1. Octal-to-Binary priority encoder(MSI)74LS148

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STIIIIIIIIYS 76543210The expression shows: if the encode input

ends are all high level, and when

ST=1(/ST=0)

YS=0.

STSTIIIIIIIIYEX 76543210

STIIIIIIII )( 76543210

It shows: when there is only one low

level(/I7=0, I7=1) at input end and

ST=1

The function table can list out:

0YEX

.SY is select output end

endextendisYEX

Ys=0 represents the circuit works

without code input.

It means when the circuit works code also

inputs.

&

&

&

&

&

I1

I2

I0

I3

I4

I5

I6

I7

S

YS

YEX

Y0

Y1

Y2

1

1

1

1

1 1

1

1 1

1 1

1 1

1

1(ST)

G1

G2

G31

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

0

1

1

11

0

1

0

1

1

0

0

0

0

6.2.2 Priority Encoder

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Ys

1 X X X X X X X X 1 1 1 1 1

0 1 1 1 1 1 1 1 1 1 1 1 1 0

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

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

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

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

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

0 X X 0 1 1 1 1 1 1 0 1 0 10 X 0 1 1 1 1 1 1 1 1 0 0 1

0 0 1 1 1 1 1 1 1 1 1 1 0 1

ST 0IN1IN 2IN 3IN 4IN 5IN 6IN 7IN 2Y 1Y 0Y EXY

endcontrolYEX :

inputselectST:

1STNo matter if there

is signal at input ends,

the circuit will not have

output. The output islocked.

The encoderworks, the

encoding output

lies on the input

variables.

0STThe encoding circuit works, encoding signalinputs, and the output of encoder is binary

complement code.

Encoder works without encoding signal input.

1,,,, 012 EXYYYY

If only there is output code

0EXY

else

1EXY

0ST

Encoder works with encoding signal inputs.

outputselectYs:

1,,,, 012 YsYYYY EX

0Ys1Ys

Octal-to-Binary priority encoder fuction table

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:07 II

02 YY

3 control terminals:ST

Input control endselect input end.Enabled at low level. If /ST=0, encoder

works in normal, if /ST=1, all the outputare locked.

:EXYExpanding end. It is used to extend

the function of encoder.

Assume: 7I

0I

The input is active-low, and the output is complement code.

7

654321

E

Y

N

S

2

10

S

Y

I7 I6 I5 I4 I3 I2 I1 I0

ST YS

Y0Y1Y2YEX74LS148

8 input ends

3 binary output ends

Select output endhas the highest priority.

has the lowest priority.

6.2.2 Priority Encoder

Block Diagram of 74148 (Octal-to-inary Priority Encoder):

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Ex: Design a hexadecimal-to binary encoder using 74148 encoders.

Then EncodeIf there is no input with

815 II

According to the priority rights

07 II

Thus , it only needs to use noencoding input YS of the 1st

encoder as select input signal

/ST of the 2nd encoder.

If there is encoding signal inputs at the 1st encoder appropriateto output 4th bit of the encoding signal, and identify the, its /YEX=0,

if there is no encoding signal input, /YEX=1, it is encoding from 8

input signals at high-bit and 8 input signals at low-bit.

The encoding input at lowest 3 bits are logic AND of /Y2/Y1/Y0 of the two encoders.

I7 I6 I5 I4 I3 I2 I1 I0

S YS

Y0Y1Y2YEX

74LS148(1)

I7 I6 I5 I4 I3 I2 I1 I0

S YS

Y0Y1Y2YEX

74LS148(2)

& & & &G 2G3 G 1 G0

Z 0Z 1Z 2Z 3

A09A A18A A27A A 36A A45AA10A11A12A13A14A15

/S 0 1 2 3 4 5 6 7 /Y2 /Y1 /Y0 /YEX YS

1 X X X X X X X X 1 1 1 1 1

0 1 1 1 1 1 1 1 1 1 1 1 1 0

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

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

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

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

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

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

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

0 0 1 1 1 1 1 1 1 1 1 1 0 1

6.2.3 Extend the Function of Encoder

Two 74148 encoders are required.

/I15 has the highest priority.

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