The University of Texas at Dallas
Computer Science Department
CS2110: Introduction to Digital Systems Laboratory
Experiment #2 – Familiarization with Common Logic Circuits; Construction of Circuits to
Represent Given Boolean Expressions
1. Introduction:
In the previous laboratory exercise, we became familiar with logic gates
which represented the three basic Boolean functions:
AND, OR, and NOT.
In this second
laboratory we will become familiar with logic gates which are much more common in
industry, and will use them, along with the circuits we have already encountered, to build a
few circuits which solve some simple Boolean expressions.
2.
Goal of this exercise:
The purpose of this lab is to familiarize students with the
functionality of the NAND, NOR, and XOR gates, all or which are more common in digital
design than the original Boolean functions OR and AND.
We will also use these logic gates
in some actual circuits.
3.
Theory of experiment:
The Boolean functions NAND, NOR, and XOR have been
discussed in class.
The basic definitions are:
•
NAND:
The output is 0 (or “low”) if
and only if (“iff”) both inputs A and B are 1 (“high”).
That is,
____
the expression
A
•
B
is 0 iff
A and B are 1.
Otherwise the output of NAND is 1.
•
NOR:
The output of NOR is 0 if inputs A or B or both is 1; it is 1 only if A and B are both 0.
•
XOR:
The output of XOR is 1 only if inputs A=1 and B=0, or A=0 and B=1; it is 0 if A and B are
both 0 or both 1.
Remember that as in the exercises in CS2110 Laboratory Exercise #1, the digital logic
circuits to be used today have inputs of nominally +5 volts for a 1, and 0 volts (technically
≤
0.7 volts) for a 0.
Likewise, circuit outputs are nominally 0 volts for 0 or false, and +5 volts
for 1 or true.
In today’s experiment, we will verify the operation of
NAND, NOR, and XOR
(74LS00, 74LS02, and 74 LS86 logic gates, respectively).
We will also put together circuits
consisting of various combinations of the six types of gates we have studied (AND, NAND,
OR, NOR, XOR, NOT) and determine their truth tables.