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2.4 Logic Gates and Logic Circuit (Logic Gates (Logic Gate: NAND (NAND…
2.4 Logic Gates and Logic Circuit
Boolean Expression
an expression that
results in a boolean value, that is either true
or false
Variables
represented by letters and can have
one of two values, either 1 or 0
Boolean operations
AND (.),
OR (+), and NOT (’)
Logical operators
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
Logical Operator
AND
It is True if and only if both of A and B are
True
Y = A • B, or Y = AB, or Y = A∩B
Truth table
OR
It is True if either A or B, or both are True
Y = A + B or Y = A ∪ B
Truth table
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
Truth table
Logic Gates
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
Logic Gate: NAND
NAND gate produce TRUE output when any of
the input is FALSE.
Produce FALSE output when all of the input
are TRUE
Y = A • B, Y = AB, or Y = A ∩ B
Logic Gate: NOR
Produce TRUE output when all of the input
are FALSE.
Produce FALSE output when any of the input
is TRUE
Y = (A + B)' or Y = (A ∪ B)'
Truth Table
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
Logic Circuit
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
