16_logic

16_logic - Introduction to Computers and Programming Prof....

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Introduction to Computers and Programming Prof. I. K. Lundqvist Lecture 16 April 28 2004 2 Today • Boolean Logic • Simplifying Formulae • Constructing Logical Statements
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Pictorial Representation of AND and OR 5 Pictorial Representation of XOR and NOT AND Inputs Output Inputs Output 0 0 0 1 1 0 1 1 0 0 0 1 OR Inputs Output Inputs Output 0 0 0 1 1 0 1 1 0 1 1 1 XOR Inputs Output Inputs Output 0 0 0 1 1 0 1 1 0 1 1 0 NOT Inputs Output Inputs Output 0 1 1 0
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6 NAND and NOR 9 1 0 0 0 A•B 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 A•B A+B B A B A PSET / / (A + B) = A • B Proving DeMorgan’s Theorem (A • B) = A + B A B Out 0 0 1 1 0 1 0 1 1 1 1 0 AB A B NAND NAND A B Out 0 0 1 1 0 1 0 1 1 0 0 0 A+B A B NOR NOR
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10 Truth Tables F 00 0 0 1 1 01 0 1 10 11 1 0 Function F is true if any of these and-terms are true! Condition that A is 0, B is 0, C is 1. OR Sum-of-Products form A•B•C A•B•C A•B•C A•B•C A•B•C F= ( ) + ( ) + ( ) + ( ) + ( ) A•B•C A•B•C A•B•C A•B•C A•B•C 11 Minterms •A minterm
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16_logic - Introduction to Computers and Programming Prof....

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