Boolean switching algebra B 布尔开关代数 Chapter 2 Basic concept Binary logic function
Boolean switching algebra 布尔开关代数 Chapter 2 Basic concept & Binary logic function
Basic Cancer R Boolean algebra(Logic algebra) is a closure mathematical system that defines a series of logic operation (and, or, not) performed on set k of variables(a, b, c.) which can only have two values of o or o Notated as L=你k,+,°-0,1} Closure(封闭) A set is closed with respect to a operator if, the operation is applied to members of the set, the result is also a member of the set
Basic Concept Boolean algebra (Logic algebra) is a closure mathematical system that defines a series of logic operation (and, or, not) performed on set k of variables (a, b, c …) which can only have two values of 0 or 1. Notated as L={k, +, •, -, 0, 1} Closure(封闭） A set is closed with respect to a operator if, the operation is applied to members of the set, the result is also a member of the set
Basic Concept Commutative properties(交换律) A+B=B+A: AB=BA Associative properties(结合律) (AB) C=A(B C):(A+B)+C=A+(B+C Distributive properties(分配率) A·(B+C)=AB+AC:A+B·C=(A+B)(A+C Complement properties(互补律) A·A'=0;A+A=1 K Identity properties (0-14) A+0=A;A-1=A;A+1=1:A0=0 idempotency property(等幂律) A+A=A:A·A=A Absorption property(吸收律) A+AB=A: A (A+B)=A
Basic Concept Commutative properties (交换律） A+B=B+A ; AB=BA Associative properties （结合律） (A•B)•C=A•(B•C) ; (A+B)+C=A+(B+C) Distributive properties（分配率） A•(B+C)=A•B+A•C ; A+B•C=(A+B)•(A+C) Complement properties（互补律） A•A’=0 ; A+A’=1 Identity properties （0－1 律） A+0=A ; A•1=A ; A+1=1 ; A•0=0 Idempotency property （等幂律） A+A=A ; A•A=A Absorption property（吸收律） A+A•B=A ; A•(A+B)=A
Basic avert R Duality property o Duals are opposites or mirror images of original operators or constants w Operator and dual or w Operator or dual and 2 Constant 1 dual O 2 Constant 0 dual 1
Basic Concept Duality property Duals are opposites or mirror images of original operators or constants. Operator and dual or Operator or dual and Constant 1 dual 0 Constant 0 dual 1
Basic Cancer R Some more important Boolean identities and theorems for convenient referral 2 A+AB=A+B, A(A'+B)=AB 顶A"=A D(A+B)=A'B':(AB)=A'+B a Demorgan's theorems 圆(A1+A2+…+A1+An)=A1'A2…A….An 0(A1A2…A1…An)=A1+A2+…+A1+.+An R AB+AB=A:(A+B)(A+B)=A o AB+A'C+BC=AB+A'C (A+B)(A+C)(B+C)=(A+B)(A+C)
Basic Concept Some more important Boolean identities and theorems for convenient referral A+A’B=A+B ; A(A’+B)=AB A’’=A; (A+B)’=A’B’ ; (AB)’=A’+B’ Demorgan’s theorems (A1+A2+…+Ai…+An )’= A1 ’•A2 ’•…•Ai ’•…•An ’ ( A1 •A2 •…•Ai •…•An )’ =A1 ’+A2 ’+…+Ai ’+…+An ’ AB+AB’=A ; (A+B)(A+B’)=A AB+A’C+BC=AB+A’C ; (A+B)(A’+C)(B+C)=(A+B)(A’+C)