Boolean Algebra simplification question

[delta59]

Homework Statement

Lets say I have 4 inputs x1 x0 y1 y0

if I have a sum-of-products say: x1x0'y1y0'+x0y1'y0

can I simplify it to x0y1'y0 by pulling out x0y1'y0 giving x0y1'y0(y0'+1) knowing that 1+y0 is 1 and 1*signalz is signalz.

Am I right in thinking this, I really don't want to do the truth table for this bad boy

thanks

 

[E_M_C]

Hi delta59,

It's pretty straightforward to simplify short Boolean expressions having 2 or 3 variables using Boolean algebra (aka the switching algebra theorems). But when you get into 4 variables or higher, or when you're evaluating lengthy expressions, it's easier to use a Karnaugh Map.

Here are some googled examples of K-maps for expressions of 4 variables.

Try doing the K-map for your expression: x_1 \cdot x_0^' \cdot y_1 \cdot y_0^' + x_0 \cdot y_1^' \cdot y_0. Does it simplify any further?