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2.4: Logic Gate and Logic Circuit (Boolean Expression, Boolean Algebra …
2.4: Logic Gate and Logic Circuit
Boolean Expression
Boolean Algebra
-Boolean Algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively
Logical Operator
Names and it symbol
Boolean Expression
• Boolean expression is an expression thatresults in a boolean value, that is either trueor false.
• Boolean expression involves values, variablesand operations.
– Variables are represented by letters and can haveone of two values, either 1 or 0.
– Boolean operations are carried out with logicaloperators.
– Logical operators in Boolean algebra are AND (.),OR (+), and NOT (’).
• Boolean expressions can be formed bycombining variables with logical operators.
• Examples of Boolean expression:
X . Y
A + B . C
(A + B)'
Logical Operator AND
• Logical AND of A and B is written as A . B andread as “A and B”.
• It is True if and only if both of A and B areTrue.
• The Boolean equation for AND operation canbe written as Y = A • B, or Y = AB, or Y = A∩B.
• The ∩ symbol is pronounced "intersection”
Truth Table for AND
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”.
Truth Table for OR
Logical Operator NOT
• The complement (or negation) of A iswritten
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=A
Truth Table
Logic Gate
• Boolean Algebra and Truth Table set out the basic principles of logic.
• Any Boolean algebra operation can be associated with a logic gate.
– AND operation AND gate
– OR operation OR gate
– NOT operation NOT 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
AND
OR
NOT
NAND
NOR
Logic Circuit
• Logic circuit is formed by combining more
than one logic gates.
• Rules in drawing a logic circuit:
– All input and output must be labelled accordingly.
– All gates must be drawn according to the
precedence of the operator.
– Crossed input lines should be drawn using jumper.
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 2
n rows
in the truth table.
• Each row will represent different combination
of input states.
Example of Logic Circuit
Example of Truth Table for Logic Circuit
