# Thread: Sum of products expansion help

1. ## Sum of products expansion help

How do I find the sum of products expansion of this Boolean function F(x,y) that equals 1 if and only if x = 1

2. 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 $x$ is the $x$'s column has 1, and $\bar{x}$ if the $x$'s column has 0. (I assumed that the negation of $x$ is denoted $\bar{x}$; you may have a different notation.) Also, you do the same for $y$. So, for the line above, you add the following product: $x\bar{y}$.

To repeat, you add all such products for lines where $F(x,y)=1$.