View the webpage here.
The purpose of this tool is to provide users a simple syntax for Boolean Algebra expressions that is as close to regular algebra syntax as possible.
Boolean Algebra syntax replaces the logical and, or, and not with *, +, and ! respectively.
In the spirit of algebraic notation, since the logical and is represented as multiplication, for such operations you can remove the * operator entirely, so that a * b is equivalent to ab.
Finally, this tool supports any level of nested parenthesis, where an expression inside parenthesis is evaluated first.
| Expression | Logical Translation |
|---|---|
| A + B | A or B |
| A * B | A and B |
| AB | A and B |
| !A | not A |
| (A+B)*C | (A or B) and C |
| (A+B)C | (A or B) and C |
| (ABC)+(!BCD) | (A and B and C) OR ((not B) and C and D) |
| (A+B+C)(!B+C+D) | (A or B or C) AND ((not B) or C or D) |
Notice the not operator in the last two examples is wrapped in parenthesis, to illustrate the order of operations.
| Evaluation Order | Boolean Algebra Operator | Logical Equivalent |
|---|---|---|
| 1st | ( ) | ( any valid expression ) |
| 2nd | ! | not |
| 3rd | * | and |
| 4th | + | or |