CSCI-150.s10
Assign #3
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Objectives:




Learn how to use and design decoders.
Learn how to design and use PLA.
Learn and practice how to design a complete logical system.
Provide appropriate documentation and good design style.
Description of the problem:
Question 1
[20 points]
Consider the following circuit with an active high output decoder. Draw a truth table for X and Y in terms
of a, b, and c.
Question 2
[20 points]
Design a decoder, with three inputs, x, y, z, and eight active high outputs, labeled 0, 1, 2, 3, 4, 5,
6, 7. There is no enable input required. (For example, if xyz = 011, then output 3 would be 1 and all other
outputs would be 0.)
The only building block is a two-input, four-output decoder (with an active high enable), the truth
table for which is shown below.
Draw a block diagram of the system using as many of these building blocks as are needed.
Question 3
[20 points]
Implement the following functions using only two of the decoders described below and two 8-input OR
gates.
F(w,x,y,z) =
G(w,x,y,z) =


m(0,4,5,6,7,12,15)
m(1,3,12,13,14,15)
CSCI-150.s10
Assign #3
EN1 EN2'
0
X
X
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
a
X
X
0
0
0
0
1
1
1
1
b
X
X
0
0
1
0
0
0
1
0
Question 4
c
X
X
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
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5
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
1
[20 points]
We need to determine whether a three-bit number, a3, a2, a1, is equal to another number, b3, b2, b1, or
if it is greater than that number. (we do not need an output for less than.)
a. Show how the 7485 would connect to accomplish this.
b. Implement this with AND and OR gates.
Question 5
[20 points]
For the following sets of functions, design a system using a PLA with number of product terms shown:
a.
b.
c.
 m(3,4,5,7)
G(A,B,C) =  m(1,3,5,6,7)
H(A,B,C) =  m(1,4,5)
F(A,B,C) =
Requirements:

All of the above designs must also be implemented using LogicWorks5, so that the correctness of all
your designed circuits could be easily verified.
You should hand in:



The documentation of your design process: formulation, including entity definition, truth tables,
and notation for the minterm form of all output functions; optimization, including reduced
equations for all outputs; and implementation, including the printout of your LogicWorks
circuit.
All of this should be handed in the HARDCOPY.
Your circuit-file (on any storage media; such as CD, memory-stick, etc.)
Cheating and Plagiarism
Columbia College expects all students to uphold the principle of academic honesty.
Cheating and plagiarism (presenting another person’s words or ideas as one’s own) are not
acceptable behavior at any academic institution. Depending on the severity of the offense such acts
can result in a grade of zero on the test or assignment, a failing grade (F) in the course or expulsion
from the College. In all cases, the circumstances and the penalty are recorded in the student’s file.