# Need help quick boolean equation

Discussion in 'Homework Help' started by romo218, Feb 14, 2007.

1. ### romo218 Thread Starter New Member

Feb 14, 2007
2
0
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)

thanks

2. ### romo218 Thread Starter New Member

Feb 14, 2007
2
0

i need it by 10:00pm tonight

3. ### chameleon New Member

Feb 16, 2007
1
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but they are not equal!

try x =1 , y=1 , z=1.

4. ### beautifulmind New Member

Mar 5, 2007
4
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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+x(y+z)
=xyz + xy +xz
=y(xz+x) +xz applying ab +a = a+b
=y(x+z) +xz
=yx+yz+xz
smile

5. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
a'b + ab' is not a + b unless the second plus is exclusive OR but
a'b + ab' + ab = a + b that I would believe

6. ### beautifulmind New Member

Mar 5, 2007
4
0
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

x'yz+xy'z+xyz'
x(y'z+yz'+x'yz
z(y+' z)+x'yz i will use +' for exlusive or
yx+' xz+x'yz
x'yz+yx+' xz
y(x'z+x) +' xz
y(x+z)+'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
xy+z(x+y)
xy+zx+zy