Computer Science 14 - Lab 1
The first lab project is to build a
multiplexor circuit. The circuit has three inputs: A, B, C,
and one output M. It works sort of like a router: if C = 0, then M is the
same as A (the value of A is routed to M); but if C = 1, then M is the same as B.
Before the lab Thursday, you should do the following tasks:
- Write the Truth Table for this function.
- Write the function in Boolean sum-of-products form, reading straight from
the table.
- Draw a Karnaugh Map for this function, and find a simpler Boolean formula.
- Show a derivation using Boolean algebra, from the complicated
to the simpler formula.
- Draw out your circuit using AND, OR, and NOT gates.
- Draw the circuit using only NAND and NOT gates.
In the Lab
- We are going to spend a few minutes
going over the various chips, boards, power supplies, and other
devices that you'll need to use for this and other labs.
- Then you will build the circuit for the Multiplexor circuit
and demonstrate your work to get credit for the lab.
Questions
Bring your answers to these questions with you to class on Friday,
to turn in. Your questions about the questions will be answered at the
beginning of class.
We can use the binary (base-two) number system to represent integers with
0/1 (bit) values. In this system, a pair of bits can be used to represent
the numbers 0 through 3, as follows.
00 = 0
01 = 1
10 = 2
11 = 3
A Comparator Circuit takes 4 inputs, (A1,A0), and (B1, B0),
which are interpreted as two base-two numbers (see the chart above).
It has two outputs, G and E. G is 1 if (A1,A0) is greater than (B1,B0),
and E is 1 if (A1,A0) equals (B1, B0).
- Write the truth table for these two functions.
- Draw Karnaugh maps for the two functions.
- Write the Boolean formulas for both functions, reading straight from the
Truth Table. Then show a derivation (mentioning the laws of Boolean
algebra that you use) to get
from the original formula to your simplified formula.
- Draw a circuit diagram for each function.