Prepared By

Asst. Lect. Mohammed Salim

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What does this course give you?

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This subject provides you with a basic understanding

of what are the digital circuits.

how they operate, and how they can be designed to

perform useful functions.

It forms the foundation necessary for the more

advanced hardware and software design courses in

this subject . You should learn about digital design

through a combination of lectures, and hands-on

laboratory.

Grading

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Course Grading:

Midterm Exam 25%

Course Work and Assignments 15%

Final Exam 60%

Total 100%

Syllabus

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Week Topic

1 Introduction to Logic Design

2 Computer Number Systems

3 Number System Conversions

4 Number System Conversions

5 Binary arithmetic

6 Binary arithmetic

7 Midterm

8 Logic Gates

9 Logic Gates

10 Boolean Algebra &Logic Simplification

11 Boolean Algebra &Logic Simplification

12 Encoders, Decoders and Multiplexer

13 Encoders, Decoders and Multiplexer

14 Flip-Flops

15 Flip-Flops

Digital Circuits

• Logic circuits are used to build computer hardware as

well as other products (digital hardware)

• Late 1960’s and early 1970’s saw a revolution in

digital capability

– Smaller transistors

– Larger chip size

• More transistors/chip gives greater functionality, but

requires more complexity in the design process

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Digital Circuits Design

Fig1: Example on transistor &

chip

• Integrated circuits are fabricated on silicon wafers

• Wafers are cut & packaged to form individual chips

• Chips have from tens to millions of transistors

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What is an IC ?

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An Integrated Circuit is a tiny electronic circuits

whose components (transistors, resistors, capacitors)

are build on the surface of a semiconductor wafer,

using the same plane fabrication technology.

Digital Circuits are Everywhere

Communications

Multi-media

Manufacturing

Consumer electronics

Health care

Defense and security

Software

Automotive, etc

(Source: R. Tummala, IEEE Spectrum, June 2006)

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Computer Number Systems

There are four computer systems :

1- Decimal number system : This system has 10

digits

{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

2- Binary number system : This system has 2 digits

{ 0, 1 }, these two digits called binary

digits or “bits”.

3- Octal number system : This system has 8 digits

8 digits { 0, 1, 2, 3, 4, 5, 6, 7 }

4- Hexadecimal: This system has 16 digits

16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D,

E, F }9 LFU 2014

Decimal Number System

5 1 2 7 4

10 1

10 0

10 -1

10 2

10 -2

500 10 2 0.7 0.04

5*102+1*10

1+20*10

0+7*10

-1+4*10

-2

=(512.74)10

Digits

Base

n 10n

-3 10-3=0.001

-2 10-2=0.01

-1 10-1=0.1

0 100=1

1 101=10

2 102=100

3 103=1000

The power of 10

Rule : d2*B2+d1*B

1+d0*B

0+d-1*B

-1+d-2*B

-2

Base = 10

10 digits= { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

}

Binary Number System

1 0 -12 -2

2 1 1/24 1/4

1 0 1 0 1

1 *22+0 *2

1+1 *2

0+0 *2

-1+1 *2

-2

=(5.25)10

(101.01)2

The Power of 2 22

21

20

2-1

2-2

Digits

Base

Base = 2 , 2 digits= { 0, 1 }

Octal Number System

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Base = 8 , 8 digits = { 0, 1, 2, 3, 4, 5, 6, 7 }

5 1 2 7 4

1 0 -12 -2

8 1 1/864 1/64

5 *82+1 *8

1+2 *8

0+7 *8

-1+4 *8

-2

=(330.9375)10

(512.74)8

82

81

80

8-1

8-2

Digits

Base

Hexadecimal Number System

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Base = 16 , 16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }

1 E 5 7 A

1 0 -12 -2

16 1 1/16256 1/256

1 *162+14 *16

1+5 *16

0+7 *16

-1+10 *16

-2

=(485.4765625)10

(1E5.7A)16

162

161

160

16-1

16-2

Digits

Base

Bit, Byte, and Nibble !

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Bit

A 'bit' (short for Binary Digit) is the smallest unit of data that can be stored by

a computer. Each 'bit' is represented as a binary number, either 1 (true) or 0

(false).

Byte

A 'byte' contains 8 bits, so for example, it could be stored as 11101001. A

single keyboard character that you type, such as the letter A or the letter T

takes up one byte of storage. letter A in binary format = 01000001 .

Nibble

This is not a very commonly used term compared to bit and byte. It is the

term given to a group of four bits. Therefore two nibbles make a byte.

Binary to Decimal Conversions

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Convert From Binary to Decimal : ( 11011001)2

Result is ( 217)10

Convert Binary fractions to Decimal ( 11.01)2 = ( 3.25)10

Binary to Decimal Conversions

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Decimal to Binary Conversions

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Decimal fraction to Binary Conversions

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Octal to Decimal Conversion

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Decimal to Octal Conversion

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Binary to Octal Conversion and vice versa

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Decimal, Binary, Octal and Hexadecimal

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Binary to Hexadecimal and Vice Versa

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Note: We take every 4 bits

and convert them to

hexadecimal

Hexadecimal to Decimal conversion

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Decimal to Hexadecimal

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