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.

Comments

THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, ...

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. ...

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high ...

sciencecapsules

Search This Blog