《数字电》英文版 chapter2-1 Boolean switching algebra

Boolean switching algebra Chapter 2 Describe switching function

Boolean switching algebra Chapter 2 Describe switching function

R A function is a term used in mathematics and logic to denote a relationshil between input and output variables R Each variable is restricted to binary(0, 1) values R The relationship is the complex of three primitive functions(And\Not\Or)

A function is a term used in mathematics and logic to denote a relationship between input and output variables. Each variable is restricted to binary (0,1) values The relationship is the complex of three primitive functions (And\Not\Or)

Describe a switching function a Truth table a Switching equation (logic equation a Logic diagram a Karnaugh maps a They are equivalent in function

Describe a switching function Truth table Switching equation (logic equation) Logic diagram Karnaugh maps They are equivalent in function

Truth table

Truth table

Atabular representation of the combinations that a group of binary input and output variables can assume oIt illustrates all of the input variable combination values and the output variables values a Number of combinations 2input

A tabular representation of the combinations that a group of binary input and output variables can assume It illustrates all of the input variable combination values and the output variables values. Number of combinations = 2input

Input output s Input A, B, C A B C R Output F 0 000 001 ■F=1 0 F0001 (0,1,1) 011 100 (100) 101 10 011 (1,1,0) (1,1,1) 111

0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 Input output A B C F 0 0 1 1 0 0 1 1 Input A,B,C ; Output F F=1 (0,1,1) (1,0,0) (1,1,0) (1,1,1)

Switching equation

Switching equation

aA switching equation defines the relationship between an output variable and a set of input variables The expression composed of logic variables and the three primitive operator [and, or, not F(A, B, C=AB+AB'C+A'BC

A switching equation defines the relationship between an output variable and a set of input variables The expression composed of logic variables and the three primitive operator [and, or, not] F(A,B,C)=AB+AB’C’+A’BC

Input output A B C F 000 R F(A, B, C=AB+ABC+A'BC 001 00 0 00011 100 0 111

F(A,B,C)=AB+AB’C’+A’BC 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 Input output A B C F 0 0 1 1 0 0 1 1

a Litera A literal is a boolean variable or its complement Product term A product term is a literal or the logical product (AND of multiple literals a Sum term A sum term is a literal or the logical OR of multiple literals s Sum of products(SOP A SOP is the logical OR of multiple product ter Each product term is the and of binary literay ms a Product of sums(POs) A POs is the logical AND of multiple product terms. each sum term is the or of binary literal

Literal A literal is a Boolean variable or its complement Product term A product term is a literal or the logical product (AND) of multiple literals Sum term A sum term is a literal or the logical OR of multiple literals Sum of products (SOP) A SOP is the logical OR of multiple product terms. Each product term is the AND of binary literal Product of sums (POS) A POS is the logical AND of multiple product terms. Each sum term is the OR of binary literal