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CSE20 Lecture 7

CSE20 Lecture 7 - CSE 20 Lecture 7 Boolean Algebra CK Cheng...

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1 CSE 20: Lecture 7 Boolean Algebra CK Cheng 2/4/2010
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Outlines Introduction Definitions Interpretation in Set Operations Interpretation in Logic Operations Theorems and Proofs Multi-valued Boolean Algebra Expression Transformations 2
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3 1. Introduction Boolean algebra is used in computers for arithmetic & logic operations. Eg: if a = 1, then y = b, else y = c. a and b values that pass through AND gates return true if and only if both a and b are true. AND Gate id a b c 0 0 0 0 1 0 1 0 2 1 0 0 3 1 1 1 a b D c
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4 OR & Inverter a and b feed into OR gates. The output is true if either a or b is true. Output c is the complement of a. OR Gate id a b c 0 0 0 0 1 0 1 1 2 1 0 1 3 1 1 1 Inverter a c 0 1 1 0 a b c a c
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5 A Half Adder: a sum D carry b a D b a D b
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6 2. Definitions Boolean Algebra: A set of elements B with two operations + (V, , OR) * ( ʌ , , AND) satisfying the following 4 laws: P1: Commutative Laws: a+b = b+a, a*b = b*a. P2: Distributive Laws: a+(b*c) = (a+b)*(a+c), a*(b+c)= (a*b)+(a*c). P3: Identity Elements: Set B has two distinct elements
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