I was wondering how one would rewrite f= x(y+z),using only AND and XOR gates, into
f=x(yz XOR y XOR z)?

xy+xz
xy(z+NOTz)+x(y+NOTy)z
x(yz+(y XOR z))

Thank you.

 

When you have:


f = A*g

and you want to show that

f = A*h

you only need to show that g = h. So you only need to show that

(y+z)=(yz XOR y XOR z)

The approach you are taking is fine.

(y+z) = (y(z+z') + (y+y')z)
(y+z) = (yz+yz' + yz+y'z)

(y+z) = (yz + (yz'+y'z))

At this point, you might make the truth table for the right hand side and that might give you a clue as to how to proceed. You might also start with the goal and see if you can work it back to the above.

(yz XOR y XOR z)

You can group this three ways:

(yz XOR (y XOR z))
((yz XOR y) XOR z)
((yz XOR z) XOR y))

So exapnd these and play with them a bit. Show what you get, even if t isn't all the way, and we'll go from there.