Boolean Algebra and Karnaugh

Question

I'm starting learning this year, Boolean algebra, truth table and Karnaugh map, on the expression below, and if any one can explain, how to pass it to table and Karnaugh map? And what are the values of 1 I get and how?

$$f(a,b)=a+\overline{a}\overline{b}$$

Thank you in advance.

Answer 1

The truth table lists all four ($2^2 = 4$) cases:

a b  |  f
-----+---
0 0  |  1
0 1  |  0
1 0  |  1
1 1  |  1

Simplified expression corresponds to the two implicant blocks shown in the map:

$f(a, b) = a \lor \lnot b$