Assignment 03
Contents:
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
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.
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Last modified: 25 January 2002