The sum of products expansion is easily obtained from the truth table. For each line of the table where the function value is 1, e.g.,
Code:
x | y | F(x,y)
--------------
....
1 | 0 | 1
....
you add one product to the sum. In this product, you write $\displaystyle x$ is the $\displaystyle x$'s column has 1, and $\displaystyle \bar{x}$ if the $\displaystyle x$'s column has 0. (I assumed that the negation of $\displaystyle x$ is denoted $\displaystyle \bar{x}$; you may have a different notation.) Also, you do the same for $\displaystyle y$. So, for the line above, you add the following product: $\displaystyle x\bar{y}$.
To repeat, you add all such products for lines where $\displaystyle F(x,y)=1$.