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2.4.1 Boolean Expression (Boolean Expression (Examples (X . Y, A + B . C),…
2.4.1 Boolean Expression
Boolean Algebra
the branch of algebra in
which the values of the variables are the truth
values true and false, usually denoted 1 and 0
respectively.
Boolean Expression
an expression that
results in a boolean value, that is either true
or false.
– Variables are represented by letters and can have
one of two values, either 1 or 0.
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– Logical operators in Boolean algebra are AND (.),
OR (+), and NOT (’).
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Logical Operators
Logical Operator AND
Logical AND of A and B is written as A . B and
read as “A and B”.
•it is True if and only if both of A and B are
True.
•The Boolean equation for AND operation can
be written as
Y = A • B, or Y = AB, or Y = A∩B
•The ∩ symbol is pronounced "intersection”.
Logical Operator OR
Logical OR of A and B is written as A + B and
read as “A or B”.
•It is True if either A or B, or both are True.
•The Boolean equation for OR operation can be
written as Y = A + B or Y = A ∪B
•The ∪symbol is pronounced “union”.
Logical Operator NOT
Logical Operator NOT
•The complement (or negation) of A is written
as A’ or and read as “not A”.
•If A is True then A’ or is False.
•If A is False then A’ or is True.
•The Boolean equation for NOT operation is
written as Y = A’ or Y =
Logic Gate
-
Gate is an electronic circuit in which the input
and output represent the statement of
Boolean algebra.
•Five basic logic gates are:
–AND gate
–OR gate
–NOT gate
–NAND gate
–NOR gate
A gate will have one or more binary
input of 0 or 1 but just one binary
output.
–AND gate -has two input and one output
–OR gate -has two input and one output
–NOT gate -has one input and one output
–NAND gate -has two input and one output
–NOR gate -has two input and one output
Truth Table
Truth Table
•A truth table is used to show the function of a
logic gate.
•It shows the output states for every possible
combination of input states.
•For a logic gate with n input, there are 2n rows
in the truth table.
•Each row will represent different combination
of input states.
The AND gate
The AND gate has two binary input and one
binary output.
•The AND gate produces a TRUE output if and
only if both A and B are TRUE.
•The Boolean expression for AND gate can be
written in three ways:
Y = A • B, Y = AB, or Y = A ∩ B.
OR gate
The OR gate has two binary input and one
binary output.
•The OR gate produces a TRUE output if either
A or B (or both) is TRUE.
•The Boolean equation for an OR gate is
written as Y = A + B or Y = A ∪B.
NOT gate
The NOT gate has one binary input and one
binary output.
•The output of NOT gate is the inverse of its
input.
TRUE input will produce FALSE, and
FALSE input will produce TRUE.
•The Boolean equation for NOT gate is written
as Y = A’ or Y =
NAND gate
Combination of AND and NOT gate.
•NAND gate produce TRUE output when any of
the input is FALSE.
•Produce FALSE output when all of the input
are TRUE.
•The Boolean expression for NAND gate can be
written in three ways:
Y = A • B, Y = AB, or Y = A ∩ B.
NOR gate
Combination of OR and NOT gate.
•Produce TRUE output when all of the input
are FALSE.
•Produce FALSE output when any of the input
is TRUE.
•The Boolean equation for an NOR gate is
written as Y = A + B or Y = A ∪B.