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Digital Electronics
Lecture 3
DeMorgan Theorem, Computer Simulation
Exercises
Lecture 3 outline
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Review of last Lecture
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DeMorgan theorems
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Simulation of Logic Gates
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Introduction to combinational logic
circuits
Review of Last Lecture
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Logic gates
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AND, OR, NOT, Ex-OR, NAND, NOR
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Truth Tables
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Boolean Algebra
DeMorgan Theorems
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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.
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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
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Consider the_ following
F = A + B_
= A + B_
= A . B_
F=A.B
Example 2 _
_
F = A _ B + AB _
= A_ B + AB
_
=A B . AB
_
_
step 1
step 2
step 3
Step 1
Step 2
=A B . AB
Step 3
DeMorgan therem can also be applied to expressions with more than two variables.
Simplification using Boolean
Algebra
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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.
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For Example: Simplify the following expression.
AB + A(B + C) + B (B + C)
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Circuit diagram using original expression
A
B
C
AB
A(B + C)
B(B + C)
AB + A(B + C) + B(B + C)
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Circuit diagram using simplified
expression
A
C
B
AC
AC + B
Simulation exercises
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Use Multisim and draw
the circuit shown in
Figure 1.
Simulate the circuit and
produce a complete truth
table for this AND gate.
VCC
5V
U1A
J1
Key = A
7408N
1.00kOhm_1%
R2
J2
R1
1.00kOhm_1%
Key = B
GND
More exercises
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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
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DeMorag Theorem
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Simplification using Boolean Algebra
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Simulation of AND, OR, NOT, Ex-OR,
NAND gates
The End
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Thank you for your
attention.