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lec6othergates

lec6othergates - CS 140 Lecture 6 Other Types of Gates...

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CS 140 Lecture 6: Other Types of Gates Professor CK Cheng 1

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Combinational Logic: Other Types of Gates Universal Set of Gates Other Types of Gates 1) XOR 2) NAND / NOR 3) Block Diagram Transfers 2
Universal Set Universal Set: A set of gates such that every switching function can be implemented with gates in this set. Ex: {AND, OR, NOT} {AND, NOT} {OR, NOT} 3

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Universal Set Universal Set: A set of gates such that every Boolean function can be implemented with gates in this set. Ex: {AND, OR, NOT} {AND, NOT} OR can be implemented with AND & NOT gates a+b = (a’b’)’ {OR, NOT} AND can be implemented with OR & NOT gates ab = (a’+b’)’ {AND, OR} This is not universal. 4
{NAND, NOR} {NOR} {XOR, AND} X 1 = X*1’ + X’*1 = X’ if constant “1” is available. 1 5

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Other Types of Gates (a) Commutative X Y = Y X (b) Associative (X Y) Z = X (Y Z) (c) 1 X = X’ 0 X = 0X’ + 0’X = X (d) X X = 0, X X’ = 1 1) XOR X Y = XY’ + X’Y XOR X Y 6
e) if ab = 0 then a b = a + b Proof: If ab = 0 then a = a (b+b’) = ab+ab’ = ab’ b = b (a + a’) = ba + ba’ = a’b a+b = ab’ + a’b = a

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lec6othergates - CS 140 Lecture 6 Other Types of Gates...

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