Boolean Functions

Lecture 2 Boolean Functions

Lecture 2
Basic Boolean functions, logic gates and
Karnaugh maps

ITP3902 Discrete Mathematics & Statistics

Page 1

Lecture 2 Boolean Functions

Logic gates
• Logic gates are digital electronic circuits in which there are only two possible states at any point, such as
• Open or close;
• High voltage or low voltage
• A certain signal is present or absent, etc.
• The two possible states are referred to as 1 or 0.
• The two states can be used to represent logic values. We use
1 to represent T(rue) and 0 to represent F(alse).
• The two states can also be used to represent one binary digit
(bit).

ITP3902 Discrete Mathematics & Statistics

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Lecture 2 Boolean Functions

Logic gates: OR gates
• An OR gate accepts two inputs and produce an output according to the following truth table.
Input

Output

A

B

A+B

0

0

0

0

1

1

1

0

1

1

1

1

• The electronic circuit symbol is
• The Boolean symbol is “+”, i.e. Q = A + B.
ITP3902 Discrete Mathematics & Statistics

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Lecture 2 Boolean Functions

Logic gates: AND gates
• An AND gate accepts two inputs and produce an output according to the following truth table.
Input

Output

A

B

AB

0

0

0

0

1

0

1

0

0

1

1

1

• The electronic circuit symbol is
• The Boolean symbol is “”, i.e. Q = AB
ITP3902 Discrete Mathematics & Statistics

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Lecture 2 Boolean Functions

Logic gates: NOT gates
•• A NOT gate or an inverter has only one input and produce an output according to the following truth table.
Input

Output

A
0

1

1

0

• The electronic circuit symbol is
• The Boolean symbol is a bar over the symbol, i.e. Q =
ITP3902 Discrete Mathematics & Statistics

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Lecture 2 Boolean Functions

Boolean Algebra and Functions
• The AND, OR and NOT functions make up a complete set to define a two valued Boolean Algebraic system.
• A binary variable is one that can only take the values 0 or 1.
• A Boolean function is an expression formed by binary variables, the