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Nagarjuna College

of Information Technology

Lab1: The AND, OR Gates

Submitted By: Checked by:

Name:

Roll No:

Class: (Teachers Name)

Date:

1/9______________________________________________________________________________________________Nagarjuna College of Information TechnologyBy Program Officer



Digital Logic Lab Manual

Lab1: The AND, OR Gates

Objectives:

To investigate AND, OR gate operation.

To study some fundamental laws of Boolean Algebra.To become familiar with logic circuits.

Introduction

This is the introductory laboratory session, to allow you to become

familiar with very basic digital circuits and the equipment that you willuse for the remainder of the experiments.

Before you even attempt this laboratory, you must have read the lab

manual. This details how you will connect components together on thebreadboard and how the inner connections of the breadboard are

structured. It also details laboratory safety information. Thedemonstrator may quiz you on your knowledge of the Laboratory

Manual.

Equipment

The equipment you require is as follows:

Your lab notebook

Your own lab kit (bought from the technicians).Power supply, Digital voltmeter (available at the desks)

Collect hook-up wire and ICs from demonstrator (74LS08 and 74LS32)

Pre-Lab Requirements

There are several tasks that you must perform prior to setting this

laboratory:

1. Read the laboratory assignment in full.2. Draw up the truth tables for a 2-input AND and a 2-input OR gate.

3. Explain the Boolean algebra Associative, Commutative and

Distributive Laws.4. Derive a Truth-Table for the function F=AB+CD.




Useful Chip Diagrams:

7408(AND) 7432(OR)

Method:

Section 1: AND Gate Implementation

(a) Connect one of the 2-input AND gates (74LS08) as shown in Figure1. Remember to power the Vcc and GND terminals of the chip.

Remember also to leave the power supply off, until you are sure thatyour circuit is wired correctly.

Figure 1: The 2-input AND gate.

(b) Vary the inputs A and B (i.e. 0 and +5V) to obtain all the possible

combinations and complete the truth table (as below) for the ANDgate. Measure the output F using a Digital Voltmeter. Give the exact

voltages that you obtained for each state of the gate.

A B F V (actual voltage)

0 0

0 1

1 0

1 1




(c) The 2-input AND gate can be extended to a 4-input AND gate as

shown in Figure 2. Connect the gates as shown and generate the

values for the truth table below.

Figure 2: The 4-input AND gate, built using 2-input AND gates.

A B C D F

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

0 1 0 1

0 1 1 00 1 1 1

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1

(d) Design a 3-input AND gate that is composed of 2-input AND gates.Measure the outputs and generate a truth table. Describe your design.

How would you create a 5 input AND gate?




Section 2: Associative and Commutative Laws

(a) Connect AND gates as shown in Figure 3 to implement the Boolean

equations F = A(BC) and G=(AB)C.

Figure 3. Proving The Associative Law.

(b) Vary inputs A, B, and C to obtain all of the possible combinations

and to check the associative law: A(BC) = (AB)C. Fill in the truth tablebelow:

A B C F G

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 11 1 0

1 1 1

(c) How would you demonstrate the Commutative Law using logicgates? Describe your design and implement it using logic gates. Check




all the combinations of inputs and the corresponding outputs to insurethat it works. Show the resulting truth table.

Section 3: Laws of Boolean algebra

(a) To demonstrate the Distributive law, connect AND, OR gates asshown in Figure 4. Vary the inputs A, B and C to obtain all possible

combinations and check that the outputs F and G are identical.

Figure 4: The Distributive Law.

Give the outputs in a truth table as shown below:

A B C F G

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0




1 1 1

Section 4: Disconnected Inputs

(a) Check the behavior of an OR gate when one of its inputs is open(disconnected - not connected to ground). Check the behavior when

two of the inputs are open. Describe what you observed. Do the same

for an AND gate.

Section 5: Boolean Equations

(a) Consider the logic statement: "If Mary obtains permission from hermother or her father and if Joe or Tom pick her up, she may go to the

cinema". This statement may be expressed as a Boolean equationusing the following Boolean variables:

F = Mary will go to the cinema (true/false)A = Her mother will give her permission (true/false)

B = Her father will give her permission (true/false) and

C = Joe will pick her up (true/false)D = Tom will pick her up (true/false)

Then F = (A+B).(C+D) is the Boolean equation that describes this

statement. Implement the circuit for this logic equation and completethe Truth Table below.

A B C D F

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 00 1 0 1

0 1 1 0

0 1 1 1

1 0 0 0

1 0 0 1




1 0 1 0

1 0 1 1

1 1 0 0

1 1 0 1

1 1 1 01 1 1 1

Section 6: Analysis of Results

(a) Are the Associative and Commutative laws obeyed in practice?

Yes

NoDon't Know

(b) The following truth table represents which Boolean equation?

A B F

0 0 0

0 1 0

1 0 1

1 1 0F = A + B

F = A.(/B)F = (/A).B

Don't know

(c) Is it possible to build an AND gate with more than 2 inputs using asingle 7408 chip?

Yes

NoDon't Know

(d) How many 2-input OR gates are required to produce an OR gate

with N inputs?

N

N+2




N-2N-1

Don't Know

Section 7: Conclusions

State briefly, but clearly, what you have gained from this assignment.Outline aspects that you have noted within the experiment outside of

the questions asked. Make comments on the procedure of the lab.


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