Boolean algebra 2 different simplification?
Wondering why the following boolean expression seem to have 2 possible simplification? Are these two both correct ? Thank you very much !
How online tutorial solves it:
How I simplify it
How online tool sovles it <--- Same as my answer
When you use a Karnaugh map you will see that they are the same. See the following Karnaugh map for this boolean expression, almost completely matched with circles:
The blue circle matches the expression BC, the red circle matches the expression B'C'. The remaining cell at AB'C still needs a circle. There are three ways to create a circle, which matches this cell:
In this solution, the cell AB'C is matched by a circle with only one cell. However this is not the biggest circle possible in this Karnaugh map. The circles chosen in a Karnaugh map are picked to be the biggest circle possible (according to the Karnaugh map rules).
The "real" other solutions are:
The green circle in this solution matches AC. The remaining third solution is this one:
The green circle in this solution matches AB'.
This means that all these three boolean expressions are equal:
BC + B'C' + AB'C(can still be more simplified, shows what happens when too small circles are choose in Karnaugh maps)BC + B'C' + AC(your solution)BC + B'C' + AB'(solution from the video)