1. De Morganâ€™s First Theorem, 2. De Morganâ€™s Second Theorem - Statement and Proof

**DE MORGANâ€™S THEOREM**

** **

The first theorem states that the
complement of the sum of two logical inputs is equal to the product of its
complements.

** **

The Boolean equation for NOR gate is

The Boolean equation for a bubbled AND
gate is

Both cases generate same outputs for
same inputs. It can be verified using the following truth table.

From the above truth table, we can conclude .

Thus De Morganâ€™s First Theorem is
proved. It also says that a NOR gate is equal to a bubbled AND gate.

The corresponding logic circuit
diagram is shown in Figure 9.47.

** **

The second theorem states that the
complement of the product of two inputs is equal to the sum of its complements.

The Boolean equation for NAND gate
is

The Boolean equation for bubbled OR
gate is

A and B are the inputs and Y is the
output. The above two equations produces the same output for the same inputs.
It can be verified by using the truth table

From the above truth table we can
conclude

Thus De Morganâ€™s First Theorem is
proved. It also says, a NAND gate is equal to a bubbled OR gate.

The corresponding logic circuit
diagram is shown in Figure 9.48

** **

Simplify the Boolean identity

AC + ABC = AC

Step 1: AC (1 + B) = AC.1 [OR law-2]

Step 2: AC . 1 = AC [AND law â€“ 2]

Therefore, AC + ABC = AC

*Circuit Description*

Thus the given statement is proved.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

12th Physics : UNIT 10a : Semiconductor Electronics : De Morganâ€™s Theorem |

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