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A boolean expression(named for mathematician George Boole) is an expression that evaluates to either true or false. Let's look at some common language examples: • My favorite color is pink. → true • I am afraid of computer programming. → false • This book is a hilarious read.
Through Boolean algebra simplification, a Boolean expression is translated to another form with less number of terms and operations. A logic circuit for the simplified Boolean expression performs the identical function with fewer logic components as compared to its original form.
A Boolean expression is a logical statement that is either TRUE or FALSE . Boolean expressions can compare data of any type as long as both parts of the expression have the same basic data type. You can test data to see if it is equal to, greater than, or less than other data.
There are a number of methods for simplifying Boolean expressions: algebraic, Karnaugh maps, and Quine-McCluskey being the more popular. We have already discussed algebraic simplification in an unstructured way. We now study Karnaugh maps (K-Maps).
You can try Wolfram Alpha as in this example based on your input:
http://www.wolframalpha.com/input/?i=((A%20OR%20B)%20AND%20(NOT%20B%20AND%20C)%20OR%20C)&t=crmtb01&f=rc
Try Logic Friday 1 It includes tools from the Univerity of California (Espresso and misII) and makes them usable with a GUI. You can enter boolean equations and truth tables as desired. It also features a graphical gate diagram input and output.
The minimization can be carried out two-level or multi-level. The two-level form yields a minimized sum of products. The multi-level form creates a circuit composed out of logical gates. The types of gates can be restricted by the user.
Your expression simplifies to C.
I found that The Boolean Expression Reducer is much easier to use than Logic Friday. Plus it doesn't require installation and is multi-platform (Java).
Also in Logic Friday the expression A | B just returns 3 entries in truth table; I expected 4.
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