CPSC 330 - Fall 2012
Homework 2
Due Monday, Oct. 8
Each student must turn in a separate set of homework solutions,
but you may work together in study groups with other students
from the class. Include the names of your study group members
on the solution set you submit.
Also, please provide sufficient space for your calculations and
answers so that grading will be easier.
Appendix C (see http://www.cs.colostate.edu/~malaiya/470/Appendix-C.pdf)
1. C.4 - Implement a two-input XOR function using AND, OR, and NOT gates.
2. C.6 - Show NAND is universal by implementing (a) two-input AND, (b)
two-input OR, and (c) one-input NOT functions with one or more
two-input NAND gates.
3. C.14 - Implement the switching element as described.
4. Finish the analysis started in class of the three-bit synchronous up/down
counter shown in http://www.electronics-tutorials.ws/counter/count_4.html.
(a) Give the three logic expressions:
JA = KA = ____
JB = KB = ____
JC = KC = ____ ____
(b) Complete the truth table with these 13 columns, where I=up/down:
I QC(t) QB(t) QA(t) | JC KC JB KB JA KA | QC(t+1) QB(t+1) QA(t+1)
--------------------+-------------------+------------------------
(c) Draw the state diagram from the truth table. Is it as expected?
5. Design a modulo-3 counter using two D flip-flops. (There is no input.)
Use a truth table with don't care values where appropriate.
QA(t) QB(t) | QA(t+1) QB(t+1)
------------+----------------
Simplify the logic expressions for the next state values, and draw the
resulting circuit.
6. Design a modulo-3 counter using two JK flip-flops. (There is no input.)
Use a truth table with don't care values where appropriate.
QA(t) QB(t) | JA KA JB KB | QA(t+1) QB(t+1)
------------+-------------+----------------
Simplify the logic expressions for the JK values, and draw the
resulting circuit.
7. C.40 - Design a 3-bit Gray code up counter using three D flip-flops.
(a) Design the circuit where "inc" is the single input and do
not include "reset". The truth table can have the form:
inc QA(t) QB(t) QC(t) | QA(t+1) QB(t+1) QC(t+1)
----------------------+------------------------
Use 4x4 Kmaps to simplify the logic expressions for the next
state values. The use of a PLA is optional; you can instead
draw individual gates in the circuit.
(b) Add the "reset" function using the technique described in
the notes.