Brock

COSC 2P12
Assignment 2

Last Modified: Sunday, 22-Oct-2017 16:45:28 EDT

Fall
2017

Due: Thursday, November 2, 2017, 4:30 pm
Accepted late until Monday, November 6, 2017, 4:30 pm, subject to a 25% penalty

1. Text Questions

3.6
3.18
3.24

2. Algebraic Form and Circuit

Manipulate the following Boolean expression in such a way so that it can be implemented using exclusive-OR and AND gates only. Draw the circuit.
AB'CD' + A'BCD' + AB'C'D + A'BC'D

3. Truth Table and Circuit

Design a combinational circuit with three inputs x, y, and z, and three outputs, A, B, and C. When the binary input formed from xyz is 0, 1, 2, or 3, the binary output produced by ABC is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input. Produce truth tables, and simplified algebraic forms, followed by circuits fot the simplified algebraic representations.

4. Truth Table to Other Forms

a. For the following Truth Table produce an algebraic representation for the outputs, f and g, in terms of the inputs a, b, c, and d.

         a b c d | f g
         _____________
         0 0 0 0 | 0 1
         0 0 0 1 | 1 1
         0 0 1 0 | 0 0 
         0 0 1 1 | 0 0 
         0 1 0 0 | 0 1
         0 1 0 1 | 0 1
         0 1 1 0 | 0 0
         0 1 1 1 | 0 0
         1 0 0 0 | 1 0
         1 0 0 1 | 0 0
         1 0 1 0 | 0 0
         1 0 1 1 | 1 0
         1 1 0 0 | 0 0
         1 1 0 1 | 0 0
         1 1 1 0 | 0 0
         1 1 1 1 | 1 1
b. Draw a logic circuit that corresponds directly to the algebraic form.
c. Simplify the algebraic form as much as possible.
d. Draw the logic circuit corresponding to the simplified form.

5. 1 MOD 4 Function

a. Produce a truth table for a function f of four inputs, a, b, c, d that is 1 when the binary number abcd modulo 4 equals 1, and is 0 otherwise.
b. Produce the corresponding algebraic expression for f.
c. Draw a logic circuit that corresponds directly to the algebraic form.
d. Simplify the algebraic form for f .
e. Draw the logic circuit corresponding to the simplified form.


Submission:
• You may either type or neatly print your solutions.
• Staple your assignment answer sheets together with a standard computer science cover sheet at the front and deposit into the hand-in box for the course. If the number of sheets makes stapling difficult please use a 9x12 envelope with a Computer Science cover page at the front to submit your assignment.