Reduce Boolean Expression

Question

Note:

A B = A and B

A + B = A or B

The expression:

r = a̅ c̅ b + a̅ c b̅ + a c̅ b̅ + a c b

Simplify?

Answer 1

It is not possible to optimize this expression further and reduce the number of terms.

The Karnaugh map:

             ab
       00  01  11  10
      +---+---+---+---+
   0  | 0 | 1 | 0 | 1 |
c     +---+---+---+---+
   1  | 1 | 0 | 1 | 0 |
      +---+---+---+---+

There are no adjacent 1 terms which can be merged into minterms with fewer literals. In fact, the expression is the three-input exclusive or of a, b and c. Output r is true if an odd number of inputs is true.