文档介绍：Boolean switching algebra
Chapter 2
Describe switching function
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 plex of three primitive functions (And\Not\Or)
Describe a switching function
Truth table
Switching equation (logic equation)
Logic diagram
Karnaugh maps
They are equivalent in function.
Truth table
A tabular representation of binations that a group of binary input and output variables can assume
It illustrates all of the input bination values and the output variables values.
Number binations = 2input
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
A switching equation defines the relationship between an output variable and a set of input variables
The posed of logic variables and the three primitive operator [and, or, not]
F(A,B,C)=AB+AB’C’+A’BC
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
Literal
A literal is a Boolean variable or plement
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.