Lesson 1100: Writing Boolean Expressions Using Electronic Gates And Using Electronic Gates to Write Boolean Expressions
Remeber that these symbols represent the Boolean operators. For
example, if you wanted to draw the Electronic gate diagram for AB or
A*B then you would use the AND gate symbol which is found below.
You then write the variables used, A and B in a column and draw lines
connecting them to the left side of the AND gate as seen below.
The last step is to label what the output will be called and in this
case we will use f
Now that you've learned how to draw a simple gate diagram, we can
move on to more complex Boolean equations. Let's draw the gate diagram
for the equation ~(A*B)+(~A). Below you will find a basic description
of steps that you should take as a beginner.
In this equation, ~(A*B)+(~A), the first half, ~(A*B), represents
A NAND B. The second half, ~A, represents NOT A. These two halves
are being OR-ed so you will need to use three gates.
In the equation there are two variables, A and B.
Since the equation has two variables, A and B, we write it down in
a column as seen below.
According to the order of operations we can do A NAND B or NOT A
first. So we draw the gates and connect them to the variables A and B
depending on what values they use. In A NAND B both A and B are being
used so we draw lines from A and B to the left side of the NAND gate.
But, NOT A only uses variable A so we draw a line from A to the NOT
gate. Look at the diagram below for better understanding.
The last operator in the equation is taking the output of A NAND B
and NOT B and OR-ing them. First draw an OR gate. Next we draw lines
from the right hand side of the NAND and NOT gate and connect them
to the left side of the OR gate as seen below
In this case the final output is f thus we draw a line from
the right hand side of the OR gate and label it f as in the
Now that you have learned the basic steps to draw a electronic
gate diagram from the equation, lets try writing a Boolean expression
from a electronic gate diagram. Given the diagram below, we will go
through the process you can take to find the Boolean expression.
From the diagram we can deduce that the equation uses two variables,
A and B, and two different gates, AND and OR.
This means that you should find parts of the equation that don't
depend on the output of any other operation. From the diagram we know
that only A AND B don't require the output of an operation.
We identified that A AND B was the only independent part of the
equation so we can write it down. Recall that you don't have to write
the '*' in an AND operation but simply put AB instead of A*B.
The only operation left is OR. This operation requires the output
of A AND B and then is OR-ed with A. Thus we take the result of AB and
OR it with A as seen below. Because of the order of operations we don't
have to put in parenthesis around the AB.
Now that you know how to draw electronic gate diagrams from equations
and equations from diagrams, try these exercises.