Chapter 4: Fundamental of
Computer Logic - IE337
Chapter 4
Fundamentals of Computer Logic
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Computer logics
• In the 1930s, Claude Shannon applied the rules of
Boole's algebra to analyze and design circuits by
algebraic means in terms of logic gates.
Chapter 4: Fundamental of
Computer Logic - IE337
• First introduced in 1854 by English mathematician
George Boole in his book An Investigation of the Laws of
Thought.
• Boolean algebra has been fundamental in the
development of computer science and digital logic.
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Chapter 4: Fundamental of
Computer Logic - IE337
Logic gate: AND
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Chapter 4: Fundamental of
Computer Logic - IE337
Logic gate: OR
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Truth table for NOT logic
gate
A
NOT (Ā)
1
0
0
1
Chapter 4: Fundamental of
Computer Logic - IE337
Logic gate: NOT
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Chapter 4: Fundamental of
Computer Logic - IE337
Logic gate: NAND
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Chapter 4: Fundamental of
Computer Logic - IE337
Logic gate: NOR
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Chapter 4: Fundamental of
Computer Logic - IE337
Logic gate: EOR
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Chapter 4: Fundamental of
Computer Logic - IE337
Basic theorms
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Chapter 4: Fundamental of
Computer Logic - IE337
Duality theorem
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
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4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
Example: Simplify X
Chapter 4: Fundamental of
Computer Logic - IE337
Example: Determine X
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
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4.6 Implementation of Boolean equations using RLL and Electronic
solid state logic gates
Chapter 4: Fundamental of
Computer Logic - IE337
Example 6: given the following Boolean
equation , sketch logic network and RLL
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4.6 Logic network design
For a given logic control sequence or truth table, It is possible to produce
the Boolean Algebra expression using the following steps:
2. For each TRUE statement associated to an output, form the logic
product (AND) of the inputs.
3. Form the logic Sum (OR) of the logic products obtained in step 2.
Chapter 4: Fundamental of
Computer Logic - IE337
1. Construct a truth table for the requested input/output
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Logic network design
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Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Combination and Sequential Networks
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Input
S
0
0
1
1
R
0
1
0
1
Output
Qn+1
Qn
0
1
Not define
Chapter 4: Fundamental of
Computer Logic - IE337
4.6 Combination and Sequential Networks
Qn+1
Qn
1
0
Not
define
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Chapter 4: Fundamental of
Computer Logic - IE337
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Chapter 4: Fundamental of
Computer Logic - IE337
CK
FF0
Chapter 4: Fundamental of
Computer Logic - IE337
FF1
FF2
FF3
1111 1110
15
14
1101
13
1100
12
1011
11
1010
10
1001
9
1000
8
0111
7
0110
6
0101
5
….
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Chapter 4: Fundamental of
Computer Logic - IE337
Problems
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B
A
C
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X
Chapter 4: Fundamental of
Computer Logic - IE337
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Chapter 4: Fundamental of
Computer Logic - IE337
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Chapter 4: Fundamental of
Computer Logic - IE337