DeMorgan’s Theorem is mainly used to solve the various Boolean algebra expressions. The Demorgan’s theorem defines the uniformity between the gate with the same inverted input and output. It is used for implementing the basic gate operation likes NAND gate and NOR gate.
The Demorgan’s theorem mostly used in digital programming and for making digital circuit diagrams.
There are two DeMorgan’s Theorems. They are described below in detail.
DeMorgan’s First Theorem
According to DeMorgan’s first theorem, a NOR gate is equivalent to a bubbled AND gate. The Boolean expressions for the bubbled AND gate can be expressed by the equation shown below.
As the NOR and bubbled gates are interchangeable, i.e., both gates have exactly identical outputs for the same set of inputs.
This equation (1) or identity shown above is known as DeMorgan’s Theorem. The symbolic representation of the theorem is shown in the figure below:
DeMorgan’s Second Theorem states that the NAND gate is equivalent to a bubbled OR gate.
This identity or equation (2) shown above is known as DeMorgan’s Second Theorem.
The symbolic representation of the theorem is shown in the figure below:
The logic circuit of the bubbled OR gate is shown below:
Here are the results when the logic circuit of bubbled OR gate when all the possible sets of inputs are applied such as 00, 01, 10 or 11.
For AB: 00
For AB: 01
For AB: 10
For AB: 11
The truth table for the bubbled AND gate is exactly identical to the truth table of a NAND gate. Hence, NAND and bubbled OR gate is interchangeable.