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Multiplication (AND) Addition (OR) Negation (NOT)
0 · 0 = 0 0 + 0 = 0 Not 0 = 1
0 · 1 = 0 0 + 1 = 1 Not 1 = 0
1 · 0 = 0 1 + 0 = 1
1 · 1 = 1 1 + 1 = 1
Note that the AND operator "· " used in Boolean Multiplication operates in a identical manner to the multiplication operator used in arithmetic. The OR operator used in Boolean addition follows the same rules used in arithmetic addition except 1 + 1 = 1 rather than 2.
The NOT operator is often written as bar above the variable.
Electronic Logic Gates
The three Gates shown schematically below are all that is required to electronically implement the three Boolean operators (AND, OR, NOT) electronically. Logic gates can be made with vacuum tubes, relays, or discrete transistors, but today gates generally reside on Integrated Circuits. Logic Gates operate in a binary mode where each input and output is in either one of two states expressed as: 0/1, True/False, High/Low or On/Off.
Truth Tables for GATES
The relationship between inputs and outputs of Gates or the effect of Boolean operators can be shown with truth tables. The truth tables for the AND, OR, and NOT operators are shown below.
As in regular algebra there are mathematical rules that must be followed. The following basic laws are the same for both Boolean and ordinary algebra.
A + B = B + A
Associative Law of Addition
A(B + C)
Associative Law of multiplication
A(BC) = (AB)C
A(B+C) = AB + AC
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circuit schematics in manual. Simulations display digital circuit operation as
one would actually see them using a logic analyzer.
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