To realize basic logic gates using universal gates.
Digital trainer kit, IC 7400, IC 7402, Connecting wires.
A universal gate is a gate which can implement any Boolean function without need to use any other gate type. The NAND and NOR gates are universal gates. In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate.
NAND gate
The NAND gate produces a LOW output when all of the inputs are HIGH. The abbreviation for this gate is NAND & the operation is same as AND followed with NOT. When any of theinputs are LOW, the output is HIGH. The standard symbol for an NAND gate is shown in figure below along with the associated TruthTable.
NOR gate
The NOR gate produces a HIGH output when all of the inputs are LOW. The abbreviation for this gate is NOR & the operation is same as OR followed with NOT. When any of the inputs are HIGH, the output is LOW. The standard symbol for an NOR gate is shown in figure below along with the associated Truth Table.
NAND Gate as a Universal Gate
To prove that any Boolean function can be implemented using only NAND gates, we will show that the AND, OR, and NOT operations can be performed using only these gates.
Implementing an Inverter Using only NAND 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)’
Implementing AND Using only NAND Gates
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)
Implementing OR Using only NAND Gates
From DeMorgan’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
NOR Gate as a Universal Gate
To prove that any Boolean function can be implemented using only NOR gates, we will show that the AND, OR, and NOT operations can be performed using only these gates.
Implementing an Inverter Using only NOR 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)’
Implementing OR Using only NOR Gates
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)
Implementing AND Using only NOR Gates
From DeMorgan’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.
Result:Thus the basic logic gates using universal gates are realized and the truth table is verified.
Q1:What are universal gates?
Ans:NAND and NOR gates are called universal gates as any type of logic gates or logic Functions can be implemented by these gates.
Q2:When the output of a NOR gate is high?
Ans:If all the inputs arelow
Q3:State De-Morgan’stheorem.
Ans:(x+y)’ =x’y’
(xy)’ = x’ + y’
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