Logic & Seq. Circuit Design
CE Department
Digital Logic Design Laboratory
National University of Science and Technology
Department of Computer Engineering
LAB MANUAL 5
Boolean Laws and DeMorgan's Theorems
Objective: Implementation of Boolean Expression through Logic Gates & also verification of
Demorgan’s Law.
Apparatus:
 Trainer board
 Connecting wires
 14 pin ICs
 7408-AND gate
 7432-OR gate
 7404-NOT gate
Summary of Theory
Boolean algebra consists of a set of laws that govern logical relationships. Unlike ordinary
algebra, where an unknown can take any value, the elements of Boolean algebra are binary
variables and can have only one of two values: 1 or 0.Symbols used in Boolean algebra include
the over bar, which is the NOT or complement; the connective+, which implies logical addition
and is read “OR”; and the connective •, which implies logical multiplication and is read “AND.”
The dot is frequently eliminated when logical multiplication is shown. Thus A • B is written AB.
The basic rules of Boolean algebra are listed in Table 7-1 for convenience
Logic & Seq. Circuit Design
CE Department
In addition to the basic rules of Boolean algebra there are two additional rules called Demorgan’s
Theorems that allow the simplification of logic expressions
Demorgan’s law can be stated in terms of logic terms, which is the 1st law states that,
(x+y)`= x`y`
And the second law state that
(xy)`= x`+ y`
Evaluation and Review questions:
1. Design circuits to prove Rules 1, 12 and Demorgan’s first law. Show the left side of the
equation as one circuit and the right side as another circuit.
2. Write the Boolean expression for this logic gate circuit, and then reduce that expression to its
simplest form using any applicable Boolean laws and theorems. Finally, prove
experimentally that both the circuits perform the same logic.
3. Suppose you needed an inverter gate in a logic circuit, but none were available. You do
however, have a spare (unused) NOR gate in one of the integrated circuits. Show how you
would connect a NOR gate to function as an inverter.
Use Boolean algebra to show that your solution is valid.
4. Use DeMorgan’s Theorem, as well as any other applicable rules of boolean algebra to simply the
following expression so there are no complementation bars extending over multiple variables:
Prove your simplification experimentally.