Computer Science – 15.2 Boolean Algebra and Logic Circuits | e-Consult

Answer:

The Karnaugh map for a 3-variable function is as follows:

We can group the '1's as follows:

• The two '1's in the first row (000 and 001) can be grouped.
• The two '1's in the fourth column (011 and 111) can be grouped.
• The '1' in the third row, second column (101) can be grouped with the '1' in the third row, third column (110).

This gives us the simplified expression: f(x, y, z) = (A'C' + A'BC) + (AB'C + ABC) = A'C' + A'BC + AB'C + ABC = A'C' + AB'C + BC

Or, using Boolean algebra: f(x, y, z) = x'z' + x'yz + xy'z + xyz