Name– study of De Morgan’s both theorems.
Aim – to study the De Morgan’s theorems and their working using logic circuits.
Apparatus – IC 7404, IC 7408, IC 7432, circuit board, power supply +5V DC, LED, connecting wires, soldering iron, cutter etc.
Circuit diagrams
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Procedure –
1) You are given IC 7404, IC 7408 and IC 7432. Identify the ICs by reading their numbers and details from above given pin configurations.
2) Connect the gates with their respective pin numbers to satisfy both De Morgan’s theorems as shown in the circuit diagrams.
3) Connect final output of the circuit to the LED.
4) Verify the truth table for each theorem by giving different combinations of logic inputs as shown the respective truth tables.
5) Write the observed truth table of each theorem and hence, write the logic equation.
Brief theory –
First theorem – it states that the complement of product is equal to the sum of the complements.
Logic equation 
Proof – we shall prove above theorem by showing that LHS & RHS of given equation are equal.
LHS =
Let A = B = 0; then = = = 1
Let A = 0 & B = 1; then = = = 1
Let A = 1 & B = 0; then = = = 1
Let A = B = 1; then = = = 0
RHS =
Let A = B = 0; then = = 1 + 1 = 1
Let A = 0 & B = 1; then = = 1+ 0 = 1
Let A = 1 & B = 0; then = = 0 + 1 = 1
Let A = B = 1; then = = 0 + 0 = 0 Thus, LHS = RHS, hence proved.
Second theorem – it states that the complement of sum is equal to the product of the complements.
Logic equation 
Proof – we shall prove the theorem by showing that LHS & RHS of given equation are equal.
LHS =
Let A = B = 0; then = = = 1
Let A = 0 & B = 1; then = = = 0
Let A = 1 & B = 0; then = = = 0
Let A = B = 1; then = = = 0
RHS =
Let A = B = 0; then = = 1.1 = 1
Let A = 0 & B = 1; then = = 1.0 = 0
Let A = 1 & B = 0; then = = 0.1 = 0
Let A = B = 1; then = = 0.0 = 0 Thus, LHS = RHS, hence proved.
Conclusion – in this way, we have studied the De Morgan’s both theorems and found that –
and
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In general, and