BE Lab Manual Experiment 2

Experiment 2

Aim: - To study and prove Demorgan’s theorem. 

Apparatus: - Demorgan’s theorem kit, patch cords,

Introduction:- The basic building block of any digital circuit is a logic gate. These logic gates operate with binary numbers. A logic gate has one or more inputs but only one output. The most basic gates are called AND gate, the OR gate and the NOT gate.

Theory:-

Demorgan’s first theorem 

Refer to Theorem (1). The following table (1) shows the truth table

The first equation describes NOR gate and second equation is a bulled AND gate. Since the outputs are equal for the same inputs, we can equate the right-hand member to get. 

It is known as Demorgan’s 1st theorem. In other words, it says that the complement of sum equals the product of complements.

NOTE: -   L.H.S. = output of NOR gate.  R.H.S. = output of bubble input AND gate. 

Demorgan’s second theorem 

Refer to Theorem (2). The above table (2) shows  the truth table

The first equation describes NAND gate and second equation is a bubbled input OR gate. Since the outputs are equal for the same inputs, we can equate the right-hand member to get. 

It is known as Demorgan’s 2nd theorem. In other words, it says that the complements of a product equal the sum of the complement.

 Procedure:-

Demorgan’s first theorem

  1. Switch ON the power supply.
  2. Select any two-bit no. (00 to 11).
  3. Apply it to two inputs A & B of OR gate (left-hand side fig.) & NOT gate (right-hand side fig.) by using patch cords. Observe the corresponding output by digital multimeter or from logic indicator provided on the kit. For the different values of A and B.
  4. You will find that if the same logic input is applied to both the figures then the output is same so it is Demorgan’s first theorem 

Demorgan’s second theorem           

  1. Select any two-bit no. (00 to 11).
  2. Apply it to two inputs A & B of OR gate (left-hand side fig.) & NOT gate (right-hand side fig.) by using patch cords. Observe the corresponding output by digital multimeter or from logic indicator provided on the kit. For the different values of A and B.
  3. You will find that if the same logic input is applied to both the figures then the output is the same so it is Demorgan’s second theorem 

Observation Table:-


Result:- Demorgan’s first and second theorems are verified.

Demorgan’s Theorem Circuit:-


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