DE MORGAN'S LAWS IN THE DIGITAL WORLD

First, we will learn the three logic operations widely used in the Digital electronic circuits.

1. Operation 'AND'
If A=1 AND if B=1, the operation 'A AND B' will also yield 1. That is, if either one of them OR both is zero, A AND B will yield No result(0).

2. Operation 'OR'
If either A OR B =1; then operation A OR B will output1.

3. Operation 'NOT'
NOT A means A is simply reversed. (A=1 changes to 0 and vice versa).
Three electronic circuits were built to execute the above operations. The DeMorgan's laws tells us that just one circuit is enough to execute all the three operations. Let us see how.

Law I : NOT (A AND B) = NOT A OR NOT B
Law II : NOT (A OR B) = NOT A AND NOT B
Laws says that AND operation can be converted into OR operation with the help of NOT. Similarly 'OR' can be turned into 'AND'

Let us now select only 'AND' operation. Combine it with NOT. That is , NOT + AND = NAND. We get a new operator called NAND. 'A' NAND 'B' means A,B is first 'ANDed' and then the result is reversed (NOT).

A B 'A'NAND'B'
0 0 1
1 0 1
0 1 1
1 1 0
We build electronic circuit to do NAND process. The circuit is called 'Logic gate'. Because it does the logic operations; takes in some inputs; let out particular voltage like a 'gate' ,( low voltage for 0; high voltage for 1.)

Using the NAND gates, we can build all other gates (like AND, OR, NOT) using De Morgan's laws. Hence one kind of logic gates (NAND) is enough. In a silicon chip (a piece of tiny sand cake), millions of NAND gates are built in. Hence the silicon wafer does the logic operations, arithmetic operations and store the results in the gates (memory). Further program and software can be built on it.
The NAND gates embedded silicon chips are found in all the smart digital gadgets like smartphones, motherboard of a computer, washing machines , lift, car and so on and on.

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