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Switching Algebra | Boolean Algebra


Switching algebra, which is also called Boolean Algebra in Digital Systems Design Arena is a special algebra designed to operate on the modern digital electronic circuits. A variable x in switching algebra can take one of the possible two values 0 and 1.

A switching Algebra is formally defined as a system consisting of the set {0,1} and three binary operations OR, AND and NOT denoted by symbols +, . and ´ respectively.

The binary operations are defined as

OR Operation

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1

AND Operation

0.0 = 0
0.1 = 0
1.0 = 0
1.1 = 0

In simpler terms, the ORing of two switching variables x and y, denoted by x+y is one of the variables x or y is equal to 1.

The AND of two switching variables x and y, denoted by x.y is equal to 0 if one of the variables x or y is equal to 0.

In switching algebra the AND combination of two variable x and y is denoted by x.y and the . sign is often omitted and is written as xy.

The Not operation is defined as follows

0’ = 1
1’ = 0

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  1. November 22nd, 2011 at 13:10 | #1

    excellent source of information for boolean logic. really helped me with a school project.