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DLD(Digital logic Design)

Prepared by:M.Atif Page 1

2014

Chenab College of

Advance Studies Toba

Tek Singh

M.cs

DLD Digital logic Design)By Sir Zohaib Hafeez


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Signal System:

Signal:

A signal is a function of

independent variables that carry some information

It is a medium on which we send or receive data.

System:

A system any physical set of component that

takes a signal, and produce a signal system from which

send or receive our data.

Signals has two types, these are

Analog signal

Digital signal

Analog signal:

A type of Signal which can through in waveform.

Digital signal:

A type of signal which can show by accurate value.


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Digital Computer and Analog

Computer:

Digital Computer:

Digital computers have made possible

many scientific industrial and commercial advances that

would have been unattainable otherwise.

Computer is used in scientific

calculation, commercial and business data processing air

traffic control and space guidance.

The general purpose digital

computer is the best-know example of a digital system.

Other examples include telephone switching exchanges,

digital voltmeters, digital counters, electronic

calculators, digital displays.

Analog Computer:

The analog computer performs a direct

simulation of a physical system. Each section of a

computer is the analog of some particular portion of the

process under study.

The term analog signal is sometimes

substituted for continuous signal because analog

computerhas come to mean a computer that manipulates

continuous variables.


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Block diagram of digital computer:

Logic Gates Types of logic gates with

truth Table:

Logic Gates:

A logic gates performs a Boolean logic

function on one or more inputs to produce a single

output. It is also called electrical logic circuits.

Gates:

Blocks of hardware that produce signals of Binary

Output Device &

Control

Input Device &

Control

Storage or

Memory unit

Control Unit Process or

Arithmetic unit


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1 or 0.The input output relationship of binary variable

for each gate can be represents in tabular from by

truth table.

Each gate has one or two binary input variable

designed by Aand B. and output represents with X.

Binary functions:

It is represented in digital computer by physical quantity

two stats represent a binary variable that can equal to 1

or 0.

AND Gate:

X=A B

A

B X

Truth Table

A B X

0 0 0

0 1 0

1 0 0

1 1 1


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OR Gate:

X=A+B

A

X

B

Truth Table

NAND Gate:

X= (AB)

A

B X

Truth Table

NOR Gate:

X=(A+B)

A

B X

A B X

0 0 0

0 1 1

1 0 1

1 1 1

A B X

0 0 1

1 0 1

0 1 1

1 1 0

A B X


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Truth Table

XOR Gate:

X=AB+AB

A

B X =AB+AB

Truth Table

XNOR Gate:

X=AB+AB

A

B X=AB+AB

Truth Table

Inverter:

0 0 1

0 1 0

1 0 0

1 1 0

A B X

0 0 0

0 1 1

1 0 1

1 1 0

A B X

0 0 1

0 1 0

1 0 0

1 1 1


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A X

Buffer:

A X

Number System:

These are disuse some type of number system.

Decimal

Binary

Octal

Hexa-decimal

Number Code:

CARY CODE BCD

ASCII

Decimal Number System:

A X

1 0

0 1

A X

0 0

1 1


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Decimal number system consist BASE 10

Its range is (0_9). Denoted by (10)

Example:1

2573)

10

= 2*103+5*102+7*101+3*100

Example: 2

25.73)

10

= 2*101+5*100+7*10-1+3*10-2

Binary Number System:

Binary number system contains Base2.Its range (0,

1).

Example: 1

101)2

=1*22+0*21+1*20

Example: 2

0.101)2

=

0*20+1*2-1+0*2-2+1*2-3

1st Binary to Decimal:

Simple value1(11001)2


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=1*24+1*2

3+0*2

2+0*2

1+1*2

0

=16+8+0+0+1

=16+8+1

= (25)10Answer

Friction value2(10.101)2

=1*21+ 0*2

0+1*2

-1+0*2

-2+1*2

-3

= 2+0+1*1/2+0+1*1/8

= 2+1/2+1/8

= 2.4+1/8 = 2.5/8 or (1.625)

Answer

2

nd

Decimal to Binary:

Simple value 1(30)10

2 30

2 15 -0

2 7 - 1

2 3 - 1

2 1 - 1

= 11110)2 Answer

Friction value 2(30.8125)10


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2 30

2 15-0

2 7-1

2 3-1

2 1-1

= (11110)2 (i)

.8125*2=1.625 1

.625*2= 1.25 1

.25*2= 0.5 0

.5*2= 1.0 1 = (1101) (ii)

= (11110.1101)2Answer

3

rd

Octal number:

Octal number consist Base 8.Its range is (0 7).

Suppose (75)8

1

st

Decimal to octal:

Simple value1(175)10

2 175

2 21-7

2 2-5

= (257)8 Answer

Friction value 2(0.15)10


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11 1

11

(1001110)2

ADDER:

Logic circuit addition which is use for binary number but

also in digital system.

Types of adder:

There are two types of adder

Half adder Full adder

Half adder:

Types of logic circuit which can add two bits

or binary number in one time and produce two bit output

name Sum and carry.

A logic circuit which have two inputs A, B and two output

Sum)and carry 0).

A Sum

BC carry

Inputs Outputs

Half Adder


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A B Co

0 0 0

1 1 0

1 0 1 0

1 1 0 1

Binary digits to Adder Sum XOR Carryout/AND

Logical Diagram:

A

B A+B)

C0 A*B)

Note:

We can also use two NDand one ORgate

instead of XORin half Adder. We can get same result

as we can get in XORgate.

Operational Diagram:

XOR

AND


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AAB

B

AB+BA

B

BA

sum

A

Carry

Note:

Behind the two AND gate two inverter are locate in

half adder

Note:

This adder cannot accept the carry from previous

addition, so this way called half adder.

Full Adder:

Logic circuit that can add 3binary number at a same time. Composed on 3

and 2 outputs 3binary number and 2 output sums and carry.

Which can shows the sequence of previous addition result. Full

adder accepts the 3 input but half adder cannot accept it.


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Inputs Outputs

C

in

A B Co

0 0 0 0 0

0

0 1 1 00 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Cin

A

B

C

Logical Diagram:

Cin

A

B C0

Two Half adder one OR gate.

Full Adder

Half adder

Half adderOR


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Boolean Expiration:

= A+ B+ Cin

C0= AB + Cin (A+B)


A XOR XOR

B

Cin AND

CoutAND

Binary Subtraction:

0 0 = 0 Borrow of 0

1 1 = 0 Borrow of 0

1 0 = 1 Borrow of 0

0 1 = 1 Borrow of 1

Sub tractor:


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A logic circuit used to Sub tractor in binary number.

Types:

Two types of sub tractor as follow

Half Subtractor

Full Subtractor

Half Subtractor:

A type of sub tractor used to sub tractor two binary numbers at a time.

Having two input and two output name

Difference

Borrow

Block Diagram:

A Di (Difference)

BB0 (Borrow out)


A Din

B

B0

Boolean Expiration:

Din = A+B

Half Subtractor


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B0= A.B

Inputs Outputs

A BD

in B0

0 0 0

1 1 1

1 0 1 0

1 1 0 0

Binary digits to Subtrct XOR NOR

Full Subtractor:

Having 3 inputs and two output are used to sub tractor 3 binary

number

Borrow in, A, B

Block Diagram:

BinDin

A

B

B

Full sub tractor


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Logical Diagram:

Bin Din

B B0


Bin Din

A

B

B0

Inputs Outputs

B

in

A B Din B0

0 0 0 0 0

1 0 0 1 1

0 0 1 1 1

1 0 1 0 1

0 1 0 1 0

1 1 0 0 0

0 1 1 0 0

1 1 1 1 1

Half sub tractorHalf sub tractorA


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Adder-subtractor:

Logic circuits which is used for addition as well as for subtraction. Acalculating machine use this system(calculator, computer).

A logic circuit in which the addition of two binary number with special

mathematic technique is equal to the difference of these two binary

numbers.

Inputs

Comparator:

F.A

F.A

F.A

F.A

Cin

Ao

Bo

A1

B1

Cin

Cin

Cin

A2

B2

A3

B3

S1S2S3


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A device which is use to show magnitude of two binary numbers. And

also use to show the comparison of two binary numbers.

Magnitude comparator & digital comparator

It is a logic circuit which is used to compare two binary numbers and

after comparison shows the magnitude rate of these two binary

numbers.

Simply show that two binary numbers are equal or not. If these

numbers are equal than comparator show the low output or 0 binary

output.

(XOR) has a capability has 1 output only when both input are not equal

and has 0 when both inputs are equal.

XOR we use the gate for comparator.

AB

High(1)

Low(0)

Low(0)

0

0

0


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Symbol or Block diagram

Logical Diagram

Combinational logic circuits:

0

1

2

3

0

1

2

3

A>B

A=B

A


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Combinational of logic gates which can presents the bolean function

without the storage capacity.

It is also called data processing circuits. Because we can process data in

these circuits. Output of these circuits is depends upon the types and

specification of logic gates that are used as a input in these circuits.

Used to solve logic problem

(Multiplexing, De-Multiplexing, Encoding, Decoding)

Multiplexer & data selector:

A combinational logic circuit which is used to combine multiple inputs

and select data from them and produce a single output. It is also Called

MUX.

Electronic circuits which is used to combine multiple input and produceonly one output.

Data selector because we also can select one input from combination

of different input.

Multiplexing:

Transmission a lot of information(multiple signal) on a smaller

line(medium).

Combinational

logic circuits

n- Input

Variablem- Output

Variable2

Multiplexer1

2

3

n

Control Signal

n = Input

m = Control Signa

I = Output


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I1I0

Examples in digital logic design:

74150 16 to 1. Multiplexer/Data selector

74151 8 to 1. Multiplexer(with inverted output)

74152 8 to 1.

74153 (Dual)4 to 1.

74157 (Dual)2 to 1.

The multiplexer use to convert parallel data to

serial data.

4 to 1 multiplexer:

Block diagram:

Truth table

S1 So y

0 0 Io

0

1 I1

1

0 12

1 1 I3

Signal Output

74153

MUX

4*1

I2

I3

Y


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Logical diagram

8 to 1 multiplexer:

8 inputs

one output & inverted output

3Data selector

1Enable input

Io

I1

I2

I3

S1

S2

Y

741520

1

2

3

4

5

6

7

Enable input/strobe

Data selector

InputsOutput


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Enable input = Strobe

1

2

4

8

5

7

6

3

Do

D1

D2

D3

D4

D5

D6

D7

Strobe


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