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lec7 - CSE 20 Lecture 7 Boolean Algebra CK Cheng 1 Outline...

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1 CSE 20: Lecture 7 Boolean Algebra CK Cheng 4/21/2011
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2 Outline Introduction Definitions Interpretation in Set Operations Interpretation in Logic Operations Theorems and Proofs Multi-valued Boolean Algebra Expression Transformations
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3 Introduction Boolean algebra is used in computers for arithmetic & logic operations. Eg: 1. if a is true, then y = b, else y = c. 2. y is true if a and b are true. 3. y is true if a or b is true.
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4 Introduction We use binary bits to represent true or false. A=1: A is true A=0: A is false We use AND, OR, NOT gates to operate the logic. NOT gate inverts the value (flip 0 and 1) y = NOT (A)= A’ id A NOT A 0 0 1 1 1 0 A A’
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5 Introduction OR gate: Output is true if either input is true y= A OR B id A B A OR B 0 0 0 0 1 0 1 1 2 1 0 1 3 1 1 1 A B A OR B
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6 Introduction AND gate: Output is true only if all inputs are true y= A AND B Id A B A AND B 0 0 0 0 1 0 1 0 2 1 0 0 3 1 1 1 A B A AND B
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7 Introduction A Half Adder: Carry = A AND B Sum = (A AND B’) OR (A’ AND B) Carry: A B Carry = A AND B
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