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

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

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

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.

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.

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)

Circuit diagram using original expression

Circuit diagram using simplified expression

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.

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.

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

The End Thank you for your attention.