POS realization of OR-AND with NOR

POS (Product of Sum) realization is a way to implement logic circuits using AND gates and OR gates. In this method, the output of multiple AND gates is fed to a single OR gate.

To realize a POS realization of OR-AND using only NOR gates, we can use the transformation method. This method involves replacing each OR gate with a combination of NOR gates and each AND gate with a combination of NOR gates and inverters.

Replacing OR gate with NOR gates

To replace an OR gate with NOR gates, we can use the following DeMorgan's theorem:

A + B = (A' * B')'

Using this theorem, we can replace an OR gate with two NOR gates. The first NOR gate will have inverted inputs, and the second NOR gate will have inverted output.

Replacing AND gate with NOR gates and inverters

To replace an AND gate with NOR gates and inverters, we can use the following DeMorgan's theorem:

A * B = (A' + B')'

Using this theorem, we can replace an AND gate with a combination of NOR gates and inverters. The number of NOR gates and inverters depends on the number of inputs in the AND gate.

For example, a 2-input AND gate can be replaced with two inverters and three NOR gates. The first two inverters will invert the inputs, and the three NOR gates will implement the AND function.

Realizing OR-AND with NOR gates

Using the above methods, we can realize any POS realization of OR-AND with only NOR gates. We can replace each OR gate with two NOR gates and each AND gate with a combination of NOR gates and inverters.

For example, a 3-input OR-AND circuit can be realized using only NOR gates as follows:

1. Replace the OR gate with two NOR gates using DeMorgan's theorem.
2. Replace each 3-input AND gate with two inverters and three NOR gates using DeMorgan's theorem.
3. Connect the outputs of all the AND gates to the inputs of the OR gates.

By using this method, we can implement any logic circuit that uses only OR and AND gates using only NOR gates.