1. DeMorgan Theorem, Computer Simulation Exercises
Digital Electronics
Lecture 3
DeMorgan Theorem, Computer Simulation Exercises

2. Lecture 3 outline DeMorgan theorems Simulation of Logic Gates
Review of last Lecture
DeMorgan theorems
Simulation of Logic Gates
Introduction to combinational logic circuits

3. Review of Last Lecture Logic gates AND, OR, NOT, Ex-OR, NAND, NOR
Truth Tables
Boolean Algebra

4. DeMorgan Theorems
DeMorgan theorems provide mathematical verification of the equivalency of the NOR and negative-AND gates and the equivalency of the NAND and negative-OR gates.
16- A + B = A_ . B_
17- (A . B) = A_ + B_
To use DeMorgan theorem in simplifying Boolean expressions, the following algorithm is needed.
1- Negate each variable.
2- Replace dots with pluses and vice versa
3- Negate the whole Boolean expression.

5. Examples Consider the following F = A_ + B = A + B_ step 1
F = A . B_ step 3
Example 2
F = A_ B + AB_
= A_ B + AB_ Step 1
=A_ B . AB_ Step 2
=A_ B . AB_ Step 3
DeMorgan therem can also be applied to expressions with more than two variables.

6. Simplification using Boolean Algebra
In the application of Boolean algebra, we have to reduce a particular expression to its simplest form and then use the simplified expression to implement our digital circuit.
For Example: Simplify the following expression.
AB + A(B + C) + B (B + C)

7. Circuit diagram using original expression

8. Circuit diagram using simplified expression

9. Simulation exercises
Use Multisim and draw the circuit shown in Figure 1.
Simulate the circuit and produce a complete truth table for this AND gate.

10. More exercises
Replace the AND gate in figure 1 by OR (74LS32), NAND (74LS00), Ex-OR (74LS86) and NOT (74LS04) gates and then produce the truth tables for such gates using Multisim.

11. Main Points DeMorag Theorem Simplification using Boolean Algebra
Simulation of AND, OR, NOT, Ex-OR, NAND gates

12. The End
Thank you for your attention.