Universal Gate
UNIVERSAL GATE
NAND and NOR gates are known as universal gates because any of these two gates is capable of implementing all other gate functions.
1. NAND Gate as a Universal Gate
The NAND gate can be used to implement the NOT function, AND
function, the OR function and other functions
also as explained below.
The NOT Gate using NAND Gate
An inverter can be made from a NAND gate by connecting all of
the inputs together and creating, in effect, a single common input, as shown in
Figure 2.10, for a two-input NAND gate. Algebraically, we may write
To construct an AND gate from NAND gates, an inverter or a NOT
gate is required to invert the output of a NAND gate. This inversion cancels out
the first inverted operation of NAND gate and the final result will be AND function
as depicted in Figure. Algebraically,
The OR Gate using NAND Gate
To construct OR function using only NAND
gates, first we transform the OR function as follows.
The above equation is implemented using only NAND gates as shown
in the Figure.
The NOR Gate Using NAND Gate
We know that Boolean expression for NOR gate is
The above equation is implemented using only NAND gates, as shown
in the Figure.
The Ex-OR Gate using NAND Gate
The Boolean expression for Ex-OR gate is given by
So, five NAND gates are required to implement the Ex-OR gate
as shown in Figure.
Ex-NOR Gate Using NAND Gate
Ex-NOR gate can be constructed by taking complement of Ex-OR.
That is, we need one more NAND gate to implement the Ex-NOR function. The figure shows Ex-NOR implementation using five NAND gates.
2. NOR Gate as a Universal Gate
Just like the NAND gate, the NOR gate also may be used to
implement all other operations of Boolean algebra. These are explained in
following texts.
NOT Gate Using NOR Gate
In the same way as the NAND gate described above, an inverter can be made from a NOR gate by connecting all of the inputs together and creating, in effect, a single common input, as shown in Figure. Algebraically,
OR Gate Using NOR Gate
An OR gate can be created by simply inverting the output of a NOR gate as shown in Figure. Algebraically,
AND Gate using NOR Gate
AND function can be generated using three NOR gates. We know that Boolean expression for AND gate is
The above equation is implemented using only NOR gates as shown
in Figure.
NAND Gate using NOR Gate
The Boolean expression for NAND gate is
The above equation is implemented using only NOR gates, as shown in Figure.
XOR function may also be implemented by using NOR gates. The Ex- OR operation is given by,
The above expression can be realized
using five NOR gates as shown in Figure.
The Ex-NOR Gate using NOR Gate
To implement Ex-NOR gate using NOR gates, we just remove the
last NOR gates from the circuit of Ex-OR gates shown in Figure.
Notes:-
REFERENCES
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