Chapter 4 Fundamental of Computer Logic IE 337

Chapter 4: Fundamental of Computer Logic - IE 337 Chapter 4 Fundamentals of Computer Logic 1

Computer logics • In the 1930 s, 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 - IE 337 • 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. 2

Chapter 4: Fundamental of Computer Logic - IE 337 Logic gate: AND 3

Chapter 4: Fundamental of Computer Logic - IE 337 Logic gate: OR 4

Truth table for NOT logic gate A NOT (Ā) 1 0 0 1 Chapter 4: Fundamental of Computer Logic - IE 337 Logic gate: NOT 5

Chapter 4: Fundamental of Computer Logic - IE 337 Logic gate: NAND 6

Chapter 4: Fundamental of Computer Logic - IE 337 Logic gate: NOR 7

Chapter 4: Fundamental of Computer Logic - IE 337 Logic gate: EOR 8

Chapter 4: Fundamental of Computer Logic - IE 337 Basic theorms 9

Chapter 4: Fundamental of Computer Logic - IE 337 Duality theorem 10

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates 11

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates 12

4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates Example: Simplify X Chapter 4: Fundamental of Computer Logic - IE 337 Example: Determine X 13

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates 14

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates 15

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates 16

4. 6 Implementation of Boolean equations using RLL and Electronic solid state logic gates Chapter 4: Fundamental of Computer Logic - IE 337 Example 6: given the following Boolean equation , sketch logic network and RLL 17

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 - IE 337 1. Construct a truth table for the requested input/output 18

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Logic network design 19

Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Combination and Sequential Networks 20

Input S 0 0 1 1 R 0 1 Output Qn+1 Qn 0 1 Not define Chapter 4: Fundamental of Computer Logic - IE 337 4. 6 Combination and Sequential Networks Qn+1 Qn 1 0 Not define 21

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CK FF 0 Chapter 4: Fundamental of Computer Logic - IE 337 FF 1 FF 2 FF 3 1111 1110 15 14 1101 13 1100 12 1011 11 1010 10 1001 9 1000 8 0111 7 0110 6 0101 5 …. 24

Chapter 4: Fundamental of Computer Logic - IE 337 Problems 25

B A C X 26 Chapter 4: Fundamental of Computer Logic - IE 337

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