| Basic
Gates and Functions
Boolean functions may be practically
implemented by using electronic
gates. The following points are
important to understand.
Electronic gates require a power
supply.
Gate INPUTS are driven by voltages
having two nominal values, e.g.
0V and 5V representing logic 0
and logic 1 respectively.
The OUTPUT of a gate provides
two nominal values of voltage
only, e.g. 0V and 5V representing
logic 0 and logic 1 respectively.
There is always a time delay between
an input being applied and the
output responding.
Logic gates
Digital systems are said to be
constructed by using three basic
logic gates. These gates are the
AND gate, OR gate and NOT gate.
There also exists other logical
gates, like the NAND, and the
EOR gates. We will only be looking
at the first three gates. The
basic operations are described
below.
AND gate
The AND gate is an electronic
circuit that gives a high output(1)
if all its inputs are high. A
dot (.) is used to show the AND
operation. Bear in mind that this
dot is usually omitted.
OR gate
The OR gate is an electronic
circuit that gives a high output
if one or more of its inputs are
high. A plus (+) is used to describe
the OR operations.
NOT gate
The NOT gate is an electronic
circuit that produces an inverted
version of the inputs logic at
its output. It is also known as
an inverter. If the input variable
is A, the inverted output is known
as NOT A.
NAND gate
This is a NOT-AND circuit which
is equal to an AND circuit followed
by a NOT circuit. The output of
all AND gates are high if any
of the inputs are low.
NOR gate
This is a NOT-OR circuit which
is equal to an OR circuit followed
by a NOT circuit. The output of
all NOR gates are high if any
of the inputs are high.
EOR gate
The Exclusive-OR gate is a circuit
which will give a high output
if either, but not both, of its
two inputs are high. An encircled
plus sign ( )
is used to show the EOR operations.
The NAND and NOR are called universal
functions since with either one
the AND and OR functions and NOT
can be generated.
Note:
A function in sum of products
form can be implemented using
NAND gates by replacing all AND
and OR gates by NAND gates.
A function in product of sums
form can be implemented using
NOR gates by replacing all AND
and OR gates by NOR gates.
the input/output combinations
for the NOT gate together with
all possible input/output combinations
for the other gate functions.
Also note that a truth table with
'n' inputs has 2n rows.
 
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