ECE190 – Spring 2009
Homework 2
(Due: 02/03/2009)
Instructions: HW will be returned to you in discussion section on Friday. Please write
the section number (AD1-AD7) that you wish your HW to be returned in. Also make sure
you staple all your papers together before dropping them in the submission box. We will
not grade any loose papers with no name or section on them.
Textbook Problems: 2.39, 2.40(a,b,d), 3.3, 3.9, 3.12, 3.22
X1. Prove that the set {NOR} is logically complete.
X2. We wish to implement two logic functions Y(a,b,c) and Z (a,b). Y is 1 in exactly
those cases where an odd number of a, b, and c equal 1. Z is the exclusive-OR of a and b.
a) Construct the truth table for Y and Z.
b) Implement the logic functions Y and Z described above using ONLY a 3-to-8
decoder and two OR gates. You can assume that you have as many inputs to each
OR gate as you find necessary.
NOTE: Problem X3 has been removed from this problem set. We will post the
solution for it later, but we will not be grading it.
X3. You are given a set of circuits to implement any 5-input, 1-output logic function
with up to 16 input combinations (equivalently, rows in a truth table) that output 1.
Explain how you can use two such circuits to implement an arbitrary 5-input logic
function. Note that you may NOT use any other logic components, only wires.
