LAB-01: Digital Logic Gates and
Boolean Functions
Objectives:
1.
To
learn about the basic logic gates – AND, OR, NOT, NAND, NOR, XOR.
2.
To
learn about the representation of Boolean functions using truth tables, logic
diagrams and Boolean Algebra.
3.
To
prove the extension of inputs of AND and OR gates using the associate law.
4.
To
familiarized with combinational logic circuits.
Apparatus:
Ø IC
7400 Quadruple 2-input NAND gates
Ø IC
7402 Quadruple 2-input NOR gates
Ø IC
7404 Hex Inverters (NOT gates)
Ø IC
7408 Quadruple 2-input AND gates
Ø IC
7432 Quadruple 2-input OR gates
Ø IC
7486 Quadruple 2-input XOR gates
Theory:
Logic gates: Logic gates are used to carry out
logical operations on single or multiple binary inputs and give one binary
output. In simple terms, logic gates are the electronic circuits in a
computerized framework or digital system. The positive supply voltage +Vs
represents true or binary 1 (ON) and 0v represent false or binary 0 (OFF).
There are several basic logic gates used in performing operations in digital
systems – OR, AND, NOT, XOR, NAND, NOR.
Truth Table: Truth Table is
used to show the result of the logical operation of a function. These
operations comprise Boolean algebra or Boolean functions. It is used to check
whether the propositional expression is true or false, according to the input
values. This is based on Boolean algebra.
Boolean algebra: Boolean algebra is the category of
algebra where the variable’s values are the truth values, true and false, meant
1 and 0. It is used to analyze and simplify digital circuits. It is also called
as Binary Algebra or logical algebra. It has been essential in the advancement
of digital electronics and is provided for in all modern programming language.
Integrated
Circuit (IC): An integrated circuit is a small chip of a semiconductor
material that mounts an entire circuit on itself. An IC can function as an
amplifier, oscillator, timer, counter, computer memory, or microprocessor. A
particular IC is categorized as either linear or digital, depending on its
intended application.
Circuit Diagram:
Experiment-01:
Experiment-02:
Experiment-03:
Data Table:
Experiment-01:
Truth table of Logic Gates.
|
Input |
AND F = A. B |
OR F = A + B |
NAND F = A. B |
NOR F = A + B |
XOR F = A ⊕ B |
|
|
A |
B |
|||||
|
0 |
0 |
0 |
0 |
1 |
1 |
0 |
|
0 |
1 |
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
1 |
0 |
0 |
0 |
|
Input A |
NOT F = A |
|
0 |
1 |
|
1 |
0 |
Experiment-02:
Truth Table for 3-input AND OR.
|
A |
B |
C |
F = ABC |
F = A + B + C |
|
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
1 |
|
0 |
1 |
0 |
0 |
1 |
|
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
0 |
1 |
|
1 |
0 |
1 |
0 |
1 |
|
1 |
1 |
0 |
0 |
1 |
|
1 |
1 |
1 |
1 |
1 |
Expressing 3-input gates as 2-input
gates using associative law.
|
F = ABC = A.(B.C) = (A.B).C |
|
F = A+B+C = A+(B+C) = (A+B)+C |
Experiment-03:
Truth
table for the given Boolean function F = A’C + AB’ + BC.
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Question and Answer:
Experiment-01:
1. The names and the numbers of the ICs that we need for:
a) 13 AND gates – IC 7408 (have 4 gates) – 4 IC
b) 12 NOT gates – IC 7404 (have 6 gates) – 2 IC
c) 15 NOR gates – IC 7402 (have 4 gates) – 4 IC
2. Your Answer
Experiment-02:
Simulation of 6-input AND gate in Logisim using only 2-input
AND gates. (Circuit)
Experiment-03:
Simulation for the given Boolean function F = A’C + AB’ + BC when the input ABC
=010
|
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IC diagram for the first implicant I1=
AC’ (Circuit)
Discussion: First of all,
we focused on the theory part. We learned about the basic logic gates, truth
table, Boolean algebra, and ICs (IC 7400, IC 7402, IC 7404, IC 4708, etc.).
For our first experiment, we build the
basic logic gates - AND, OR, NOT, NAND, NOR, XOR on Logisim. We observe the
outputs, collected the data in the truth table for all combinational input.
Then We came into our second experiment and constructed 3-input AND & OR gates from 2-input AND & OR gates. Then we took all the output for different input in the truth table and expressed it using associative law. We also Simulate 6-input AND gates in Logisim using only 2-input AND gates. (Circuit)
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