Need help quick boolean equation

Thread Starter


Joined Feb 14, 2007
Hey, i have this equation and i need to simplify it:
x'yz + xy'z + xyz'

i know it = xy + xz + yz
i just dont know how to get there

Its for when exactly 2 inputs are high

i have tried many ways and i cant find out the right way.

i need the way of getting it using laws and theorems, not the other grid way (cant remember name)

Double check on this because i have done this ages ago since graduation

x’yz + xy’z +xyz’

=x’yz +x(y’z+yz’) => use truth table to prove that a’b+ab’= a +b or u may use Boolean algebra
=x’yz + xy +xz
=y(x’z+x) +xz applying a’b +a = a+b
=y(x+z) +xz
:) smile
yes i chose the sign +' i forgot the symbol usually we draw a circle around the + but u dont have amathematical editor in this forum and they are available u may add it

i will put it in red color as well, the previouse solution was short

Knowing shanon x+' y = xy' + x'y

z(y+' z)+x'yz i will use +' for exlusive or
yx+' xz+x'yz
x'yz+yx+' xz
y(x'z+x) +' xz
xy+xz +' xz
xy + z(x'y +xy') by shanon
xy +zxy'+zx'y by expantion
x(y+zy') + zx'y
x(y+z) +zx'y
xy +xz +zx'y