# physics 201 - La Salle University

```PHYSICS 201
FALL 99
LAB 10
Part 1. The AND gate.
Simulate the circuit below. The new item is an AND gate (found under the logic gates
button in Electronics Workbench). Right click on it and choose Component Properties;
under the Models tab, select Library ttl and Model LS (which is just a particular kind of
AND gate). Fill in the truth table below by connecting A and B to the high and low
lines.
A
Low (0)
Low (0)
High (1)
High (1)
B
Low (0)
High (1)
Low (0)
High (1)
Voltage
High or low
Part 2. De Morgan’s Theorem.
De Morgan’s Theorem (p. 52, Introduction to Digital Systems) states that
AB = (A΄ + B΄)΄
A + B = (A΄B΄)΄
where AB means A AND B, A + B means A OR B and A΄ means NOT A. In other
words, you can construct the equivalent of an AND gate using NOTs and ORs, and you
can construct the equivalent of an OR gate using NOTs and ANDs. Do just that  in
Electronics Workbench build an AND using NOTs and ORs, then build an OR using
NOTs and ANDs. Paste the circuit in this document.
Part 3. All from NAND.
We discussed in class how all logical circuits could be built using only NAND gates.
Build an OR gate using only NANDs. Place a copy of it in this document.
Part 4. Converting Binary Representation to Gray Code.
There is more than one way to use 1s and 0s to represent decimal numbers. Two
common representations (binary and gray code) are shown in the table below.
Decimal
0
1
2
3
4
5
6
7
Binary Representation
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
Gray Code
D
0
0
0
0
1
1
1
1
E
0
0
1
1
1
1
0
0
F
0
1
1
0
0
1
1
0
The binary representation used for doing mathematics (adding, multiplying and so on).
Gray code has the useful property that adjacent decimal numbers differ by at most one
bit.
Let use build the circuitry that converts binary representation to gray code. First build a
circuit that has three inputs, A, B and C and one output D. Start off with the expression
for the output D
D = AB′C′ + …
Simplify the expression and then build the simplified circuit. Repeat these steps for
outputs E and F. If the expression above does not simplify, you will need a three-input
AND. You can achieve this end by right clicking on an AND, choosing Component
Properties and then the Number of Inputs tab. Paste the circuits in this document.
Now build the circuitry that converts the other way, gray code to binary. Start off with
A= DEF′ + …
And so on.
```