Expression Form Types

Example: Here is the truth table for some expression $E$:

$x$	$y$	$z$	$E$
$0$	$0$	$0$	$0$
$0$	$0$	$1$	$0$
$0$	$1$	$0$	$1$
$0$	$1$	$1$	$1$
$1$	$0$	$0$	$0$
$1$	$0$	$1$	$0$
$1$	$1$	$0$	$0$
$1$	$1$	$1$	$1$

To write the expression in a sum-of-products form, we look at all the cases when the expression $E$ is true (= equal to $1$,) which happen when: (1) $x = 0, y = 1$, and $z = 0$; (2) $x = 0, y = 1$, and $z = 1$; and (3) $x = 1, y = 1$, and $z = 1$.