CHAPTER 2: Boolean SwitchingAlgebra（布尔开关代数）Introduction:Boolean algebra is a mathematical system thatdefines a series of logical operations (ANDOR, NOT) performed on sets of variables(a, b, C...... ).When stated in this form , theexpression is called a Boolean equationorswitchingequation
Introduction： Boolean algebra is a mathematical system that defines a series of logical operations (AND, OR, NOT) performed on sets of variables (a, b, c,. ).When stated in this form , the expression is called a Boolean equation or switching equation. CHAPTER 2: Boolean Switching Algebra(布尔开关代数)
Three Primitive Logic Function---AND"0", " *", "",no spaceOperatorSymbols:S=x yS=x*ys=(x) (y)TwoinputandtruthtablexSLOutputInput8xyS=X.Y000xY010Z010S=X.Y.Z111WXtDistinctiveshapesymbolsforANDgate7S=WX-YZ
Three Primitive Logic Function -AND Operator Symbols: “()”, “ * ”, “ ·”,no space S=x y s=x*y s=(x) (y) Two input and truth table Distinctive shape symbols for AND gate Input Output x y z 0 0 0 0 1 0 1 0 0 1 1 1 X Y S S = X ·Y X Y Z S S = X ·Y ·Z X Y W Z S S = W ·X ·Y ·Z S
Three Primitive Logic Function----OR“"+""OperatorSymbols:S=x + yTwoinputand truth tablexSOutputInputS=X+YsXyxY000Sz011S=X+Y+Z011WX111SYDistinctiveshapesymbolsforORgateS=W+X+Y+Z
Three Primitive Logic Function -OR Operator Symbols: “+” s=x + y Two input and truth table Distinctive shape symbols for OR gate Input Output x y z 0 0 0 0 1 1 1 0 1 1 1 1 X Y S S = X + Y X Y Z S S = X + Y + Z X Y W Z S S = W + X + Y + Z S
Three Primitive Logic Function-----NOT99<61OperatorSymbols?X=X，X=X'truthtable+4OutputInputX'x01PX01DistinctiveshapeoftheNOTsymbols
Three Primitive Logic Function -NOT Operator Symbols: “ ”，“ ” x=x ，x=x truth table Distinctive shape of the NOT symbols Input Output x s 0 1 1 0 X X′ X X′ ׳ ׳ x ׳
Derived logic functions ------NANDNOR.EX-OR.EX-NOR NAND (not and): s=(xy) ; S=X yXSYOutputInputSxyS-(XY)ors=XY001011011SY011S=(XY)ors=XY
Derived logic functions -NAND 、 NOR、EX-OR、EX-NOR NAND (not and)：s=(x y)׳ ; s=x y X Y S S =(X Y) or s =X Y Y X S S =(X Y) or s =X Y Input Output x y S 0 0 1 0 1 1 1 0 1 1 1 0