Logic Design Course for 1st year IT students

1. Prepared By
Asst. Lect. Mohammed Salim
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LFU 2014

2. What does this course give you?
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.



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3. Grading
Course Grading:

Midterm Exam
Course Work and Assignments
Final Exam
Total
3
25%
15%
60%
100%
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4. Syllabus
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4
Topic
Introduction to Logic Design
Computer Number Systems
Number System Conversions
Number System Conversions
Binary arithmetic
Binary arithmetic
Midterm
Logic Gates
Logic Gates
Boolean Algebra &Logic Simplification
Boolean Algebra &Logic Simplification
Encoders, Decoders and Multiplexer
Encoders, Decoders and Multiplexer
Flip-Flops
Flip-Flops
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5. 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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6. 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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7. What is an IC ?
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.
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8. Digital Circuits are Everywhere
(Source: R. Tummala, IEEE Spectrum, June 2006)
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Communications
Multi-media
Manufacturing
Consumer electronics
Health care
Defense and security
Software
Automotive, etc
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9. 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, LFU 20149, A, B, C, D,
7, 8,
9


10. Decimal Number System
The power of 10
Base = 10
10 digits= { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
}
n
10n
-3
10-3=0.001
Base
10 2 10 1 10 0
-2
10-2=0.01
Digits
5 1 2
-1
10-1=0.1
0
100=1
1
101=10
2
102=100
3
103=1000
500
10
2
-2
10 -1 10
7 4
0.7 0.04
5*102+1*101+20*100+7*10-1+4*10-2
=(512.74)10
Rule :
d2*B2+d1*B1+d0*B0+d-1*B-1+d-2*B-2

11. Binary Number System
Base = 2 ,
The Power of 2
2 digits= { 0, 1 }
Digits
22
21
20
2-1
4
Base
2
1
1/2 1/4
1 0 1
0 1
2
-1
1
0
2-2
-2
1 *22+0 *21+1 *20+0 *2-1+1 *2-2
=(5.25)10
(101.01)2

12. Octal Number System

Base = 8 , 8 digits = { 0, 1, 2, 3, 4, 5, 6, 7 }
81
80
8-1
64
Base
82
8-2
8
1
1/8 1/64
5 1 2
7 4
2
Digits
-1
1
0
-2
5 *82+1 *81+2 *80+7 *8-1+4 *8-2
=(330.9375)10
(512.74)8
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13. Hexadecimal Number System

Base = 16 ,
16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }
162 161 160
Base
16-1
16-2
256
1
1
E
5
7
A
2
Digits
16
1/16 1/256
1
0
-1
-2
1 *162+14 *161+5 *160+7 *16-1+10 *16-2
=(485.4765625)10
(1E5.7A)16
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14. Bit, Byte, and Nibble !

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.
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15. Binary to Decimal Conversions

Convert From Binary to Decimal : ( 11011001)2
Result is ( 217)10
 Convert Binary fractions to Decimal ( 11.01)2 = ( 3.25)10
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16. Binary to Decimal Conversions
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17. Decimal to Binary Conversions
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18. Decimal fraction to Binary Conversions
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19. Octal to Decimal Conversion
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20. Decimal to Octal Conversion
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21. Binary to Octal Conversion and vice versa
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22. Decimal, Binary, Octal and Hexadecimal
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23. Binary to Hexadecimal and Vice Versa
Note: We take every 4 bits
and convert them to
hexadecimal
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24. Hexadecimal to Decimal conversion
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25. Decimal to Hexadecimal
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