EXPERIMENT:
2 Verification of all gates using UNIVERSAL GATES
AIM:- (a). To study and
verify the all logic gates using UNIVERSAL Gate NAND.
LEARNING
OBJECTIVE:-
Identify NAND ICs and their specification.
COMPONENTS
REQUIRED:-
Logic gates (IC)
trainer kit.
Connecting patch
chords or wires.
IC 7400
THEORY:
NAND gate is actually
a combination of two logic gates: AND gate followed by NOT gate. So its output
is complement of the output of an AND gate.
This gate can have
minimum two inputs, output is always one. By using only NAND gates, we can
realize all logic functions: AND, OR, NOT, X-OR, X-NOR, NOR. So this gate is
also called universal gate.
(1). NAND gates as NOT gate
A NOT produces complement of the
input. It can have only one input, tie the inputs of a NAND gate together. Now
it will work as a NOT gate. Its output is
Y = (A.A)’
=> Y
= (A)’
(2). NAND
gates as AND gate
A NAND
produces complement of AND gate. So, if the output of a NAND gate is inverted,
overall output will be that of an AND gate.
Y
= ((A.B)’)’
=> Y
= (A.B)
(3). NAND gates as OR
gate
From De-Morgan’s
theorems: (A.B)’ = A’ + B’
=> (A’.B’)’
= A’’ + B’’ = A + B
So, give
the inverted inputs to a NAND gate, obtain OR operation at output.
(4). NAND
gates as X-OR gate
The
output of a two input X-OR gate is shown by: Y = A’B + AB’. This can be
achieved with the logic diagram shown in the left side.
Gate
No. Inputs Output
1 A,
B (AB)’
2 A,
(AB)’ (A
(AB)’)’
3 (AB)’,
B (B
(AB)’)’
4 (A
(AB)’)’, (B (AB)’)’ A’B + AB’
Now the
output from gate no. 4 is the overall output of the configuration.
Y = ((A
(AB)’)’ (B (AB)’)’)’
= (A(AB)’)’’
+ (B(AB)’)’’
= (A(AB)’)
+ (B(AB)’)
= (A(A’
+ B)’) + (B(A’ + B’))
= (AA’
+ AB’) + (BA’ + BB’)
= (
0 + AB’ + BA’ + 0 )
= AB’
+ BA’
=> Y = AB’
+ A’B
(5). NAND gates as NOR gate
A NOR
gate is an OR gate followed by NOT gate. So connect the output of OR gate to a
NOT gate, overall output is that of a NOR gate.
Y
= (A + B)’
Procedure:
- Connect the trainer
kit to ac power supply.
- Connect the NAND gates
for any of the logic functions to be realized.
- Connect the inputs of
first stage to logic sources and output of the last gate to logic
indicator.
- Apply various input
combinations and observe output for each one.
- Verify the truth table
for each input/ output combination.
- Repeat the process for
all logic functions.
- Switch off the ac
power supply.
RESULT:
AIM:- (b). To study and
verify the all logic gates using UNIVERSAL Gate NOR.
LEARNING
OBJECTIVE:-
Identify NOR ICs and their specification.
COMPONENTS
REQUIRED:-
Logic gates (IC)
trainer kit.
Connecting patch
chords or wires.
IC 7402
Theory:
NOR gate
is actually a combination of two logic gates: OR gate followed by NOT gate. So
its output is complement of the output of an OR gate.
This gate
can have minimum two inputs, output is always one. By using only NOR gates, we
can realize all logic functions: AND, OR, NOT, X-OR, X-NOR, NAND. So this gate
is also called universal gate.
(1). NOR gates as NOT gate
A NOT
produces complement of the input. It can have only one input, tie the inputs of
a NOR gate together. Now it will work as a NOT gate. Its output is
Y = (A+A)’
=> Y = (A)’
(2).NOR
gates as OR gate
A NOR
produces complement of OR gate. So, if the output of a NOR gate is inverted,
overall output will be that of an OR gate.
Y
= ((A+B)’)’
=> Y
= (A+B)
(3). NOR
gates as AND gate
From De-Morgan’s
theorems: (A+B)’ = A’B’
=> (A’+B’)’
= A’’B’’ = AB
So, give
the inverted inputs to a NOR gate, obtain AND operation at output.
(4).
NOR gates as X-NOR gate
The
output of a two input X-NOR gate is shown by: Y = AB + A’B’. This can be achieved
with the logic diagram shown in the left side.
Gate
No. Inputs Output
1 A,
B (A
+ B)’
2 A,
(A +
B)’ (A
+ (A+B)’)’
3 (A
+ B)’,
B (B
+ (A+B)’)’
4 (A
+ (A + B)’)’, (B +
(A+B)’)’ AB
+ A’B’
Now the
ouput from gate no. 4is the overall output of the configuration.
Y = ((A
+ (A+B)’)’ (B +( A+B)’)’)’
= (A+(A+B)’)’’.(B+(A+B)’)’’
= (A+(A+B)’).(B+(A+B)’)
= (A+A’B’).(B+A’B’)
= (A
+ A’).(A + B’).(B+A’)(B+B’)
= 1.(A+B’).(B+A’).1
= (A+B’).(B+A’)
= A.(B
+ A’) +B’.(B+A’)
= AB
+ AA’ +B’B+B’A’
= AB
+ 0 + 0 + B’A’
= AB
+ B’A’
=> Y = AB
+ A’B’
(5). NOR
gates as NAND gate
A NAND
gate is an AND gate followed by NOT gate. So connect the output of AND gate to
a NOT gate, overall output is that of a NAND gate.
Y
= (AB)’
Procedure:
- Connect the trainer
kit to ac power supply.
- Connect the NOR gates
for any of the logic functions to be realized.
- Connect the inputs of
first stage to logic sources and output of the last gate to logic
indicator.
- Apply various input
combinations and observe output for each one.
- Verify the truth table
for each input/ output combination.
- Repeat the process for
all logic functions.
- Switch off the ac
power supply.
Precautions:
·
All IC’s must be checked before start the
experiment.
·
All connections should made and tight.
·
While making connections main voltage should
be kept switch off.
·
The circuit should be OFF before change the
connection.
RESULT: -
