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TongLecture5 - CS281 Lecture 5 Tuanjie Tong Last Class...

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CS281 Lecture 5 Tuanjie Tong
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Last Class: Introduction to boolean algebra Boolean Function This class: Algebraic manipulation Canonical forms Standard forms
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Boolean Function Formed from variables, operators, parentheses, and equal sign. Example: F1= xy+yz+x’y’z Order of computation: parentheses, NOT, AND, OR.
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Boolean Function (cntd…) Terminologies: OR term, AND term, literal (variable or its complement)
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Define a Boolean Function by Truth Table Row Number x y z F 1 F 1 0 0 0 0 0 1 1 0 0 1 1 0 2 0 1 0 0 1 3 0 1 1 1 0 4 1 0 0 0 1 5 1 0 1 0 1 6 1 1 0 1 0 7 1 1 1 1 0
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Truth Table Suppose number of variables (not literals)=n 2 n rows Each row has different variable values Could be numbered by the binary numbers represented by the variable values
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Complement of a Function F -> F’: AND->OR, OR->AND, and replace every LITERAL with its complement, also add the implicit parentheses from F Example: F=xy+yz+x’y’z -> F’=(x’+y’)(y’+z’)(x+y+z’)
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Algebraic Manipulation Same function can be specified by two or more different algebraic expressions. To prove two expressions define the same function: By truth table By algebraic manipulation
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Algebraic Manipulation (cntd…) Example: – F 1 =xy+xy’z+x’yz F 2 =xy+xz+yz Do they represent the same function?
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