COMP 150, Assignment 03, Spring 2002

Assignment 03

Overview

Topic: Boolean Logic and Gates
Related Reading: Ch. 1.1 of [Br]; Mod. 7.1, 7.2, and skim 7.3 of [DH]
Due: 8pm Thursday, 7 February 2002

This assignment will use the Logg-O software from the Decker/Hirshfield text. The practice problems will include an introduction to using the software. Also, please see the following information regarding using the Decker/Hirschfield software.

Internet Requirements

While doing this assignment, you will either need to use an internet connection or else the CD-ROM that comes with the DH text.

Practice Problems

Question 1 of Ch. 1.1 (p. 24 [Br])
answers appear in Appendix F

Complete Lab 7.1 [DH pp. 241-242]. This lab walks you through the use of their Logg-O software, which we will be using for this assignment.

Complete Lab 7.2 [DH pp. 245-246]. This lab lets you start building some interesting circuits (some of which may look familiar from lecture).

Problems to be Submitted (20 points)

(3 points)
Problem 2 of Ch. 1 (p. 70 [Br])
[You do not need to submit any Logg-O files for this problem. In fact, you do not even need to use Logg-O to determine the answer.]
(3 points)
Create a circuit in Logg-O that implements the following statement:
(a AND (NOT (a OR (NOT b))))
Save it in a file named "Circuit" for submission.
(2 points)
Explain why the circuit you have created in the previous question is unnecessary. Specifically, report the output value of the circuit for each of the four possible input combinations.
(2 point)
A majority circuit with three inputs is a circuit with a single output which is set to 1 whenever two or more of the inputs are set to 1.
There are eight possible combinations for the input settings. Please give a logic table which lists all eight combinations along with the output setting for each case.
(An example of formatting such a logic table is given in Exercise 2b on p. 266 of [DH].)
(4 points)
Construct a circuit which implements majority function with Logg-O. After testing its validity, save it in a file named "Majority" for submission.
(2 points)
Figure 7.7 on page 244 of [DH] shows a circuit for a one-bit adder. This circuit can be made significantly simpler, however, by using an XOR gate, as the resulting 'sum' bit is precisely (a XOR b). Build this simpler version using Logg-O. Test it using all possible combinations of inputs.
When you are satisfied, save your circuit in a file named "HalfAdd" for submission.
(4 points)
Figure 7.8 on page 244 of [DH] shows how two half-adders can be used to build a full-adder. Use the principals of the previous problem to build a full-adder circuit.
When you are satisfied, save your circuit in a file named "FullAdd" for submission.

Overall, you should submit five files. #2, #4, #6, and #7 each require the submisison of a saved Logg-O session. The remainder of your answers should be typed in a single document to be submitted.

Extra Credit (3 points)

Interestingly, any given boolean function can be calculated by a circuit consisting solely of NAND gates.

Create a circuit, using only NAND gates, which has the same overall behavior as a NOT gate. That is, your circuit should have one input switch and one output light, and the light should be on precisely when the switch is off. Save your circuit in a file named "ExtraNot" to be submitted.

Create a circuit, using only NAND gates, which has the same overall behavior as an AND gate. That is, your circuit should have two input switches and one output light, and the light should be on only in the case with both input switches are on. Save your circuit in a file named "ExtraAnd" to be submitted.

Create a circuit, using only NAND gates, which has the same overall behavior as an OR gate. That is, your circuit should have two input switches and one output light, and the light should be on so long as at least one of the input switches is on. Save your circuit in a file named "ExtraOr" to be submitted.

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