BOOLEAN FUNCTION SIMPLIFICATION
Most undergraduate computer science programs require the study of digital
logic. Besides just understanding how a digital computer works, it is also
important to understand how digital circuits can be simplified so that they
will be faster and cost less. A couple of ways to do this is by using Boolean
Algegra and Karnaugh Maps. The Java program on this web page will allow the
user to simplify Boolean expression that have up to five variables. This can
be used to check your work to see if you obtain the same answers when you
try to simplify Boolean expression on your own. This is particularly
important when you do some of the laboratories. Make certain you have the
correct functions before starting on the lab itself.
In some cases the simplified Boolean expressions are not unique. This
program presents one answer. For the case when there is not a unique answer
the number of terms and the number of variables they contain should be
identical, but the terms themselves may be different.
This program allows the user to simplify Boolean/binary function
expressions. Click one of the radio keys: Keyboard input, Karnaugh input or
Truthtable input and then click the OK button. The three methods of input are:
The Java code for this page was completed on September 13, 1998. It has been
been tested, but not exhaustively. I have found a couple of mistakes and they
have all been corrected. I am fairly confident that it now works correctly.
Currently one can type in 5 variables using the
Keyboard input or the truthtable input. I haven't figured out
how to allow the user to input 5 variables when using the Karnaugh map
- Keyboard input: The expression is typed in using single letter
variable names. Up to 5 variables are allowed to be used in an expression.
A single quote ("'") after a variable is used to
indicate that the variable is negated. Plus signs ("+") are used to
join together terms. Each term need not have all variables. Press return
after the entire function expression has been typed into the window.
- Karnaugh input: The variable names (again single letters) are input in a
window to determine their names and how many variables there are. There
may be spaces in the list of variables. Up to four variables are allowed
for this input method. Press return and the Karnaugh map
will be displayed. Click with the mouse to change between a 0 and 1 in
each cell of the map. Click the accept button after all cells have been
- Truthtable input: The variable names (again single letters) are input
in a window to determine their names and how many variables there are.
There may be spaces in the list of variables. Up to five variables are
allowed for this input method. Press return and the
truthtable will be displayed. Click with the mouse to change between a
0 and 1 in each cell for the function. Click the accept button after
all cells have been set.
Soon a paper discussing the algorithm can be reached using this link:
An Algorithm for Simplifying Digital
Date Page last modified and links checked: September 13, 1998
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