EE 162L
EE Dept - NMT
Prelab: The next level of logic
Expanding on your knowledge of digital logic
In the first digital logic lab you learned about three Boolean operators, NOT, AND, and OR. You also
learned that there is a gate representation of each, and that there are physical devices that perform these
operations. The next step is to learn how to assemble them into a functional system of logic. Be aware
that things can go from simple and fun, to complex and confusing very quickly here, so take it slow. Also
be careful about asking the Internet for help on this subject, as there are many rabbit holes you can get
lost in. That said, feel free to ask away but be prepared to find yourself lost very quickly. Try to keep it simple.
Let's start with the Boolean expression below. You know that Boolean expressions share some of the
symbols you are familiar with but understand that they mean different things here.
$$F = AB + \overline{A} \overline{B}$$
The expression reads as "F equals A AND B OR NOT-A AND NOT-B" and the truth table for this
expression is as follows.
ABF
0 0 1
0 1 0
1 0 0
1 1 1
There is a direct connection between the expression and the truth table. We can see that there is a 1 in the
F column in two places, the first is where A and B are both 0's, or NOT'd, and the second is where A and
B are both 1's. All other combinations of A and B result in F being 0. Given an expression, it is simple to
generate an equivalent truth table.
The next step is to create a digital logic circuit that represents the logic expression. This is done very
literally. Start by ANDing together A and B. Next AND AB, similar to the last but both A and B are
NOT'd. Lastly the outputs of the ANDs are OR'd together. See the circuit below.
B
AB
08
A
04
A
AB
08
B
04
B
32
F = AB + AB
This concludes the lesson. Now it's time to give it a try on your own.
Using your own logic
Given the logic expression $$F = \overline{A}BC + A\overline{B}C + ABC$$, create the equivalent truth table and draw the logic
circuit that represents the expression.
Note: In this problem there are 3 variables. You should be able to expand what you have learned to deal
with them. Try to think through it but if you get stuck, ask for help.
Another Note: When drawing your logic circuit, make it as neat as you are able and label it completely.
Hint: My circuit is labeled completely.
