Realizing f=yz+(x'+z')w with 4, 2 Input NAND Gates

[James889]

Hi,

I need to realize the function f = yz + (x'+z')w
using 4, 2 input NAND gates.

The function can be written in the appropriate form like so:

f = yz+wx'+ wz'
f ' = (y'+z')(w'+x)(w'+z)
(f ')' = (y'+z')'(w'+x)'(w'+z)'

Its just that i don't know how to to it when you are required to use 4 of them.

//james

 

[LCKurtz]

Try implementing your original function, unchanged, with OR and AND gates. That will use four gates. Then put inverter bubbles in front of the OR gate that has x' and z' as its inputs, changing them to x and z. Then put inverter bubbles on the right of both AND gates and on the left on the remaining OR gate, which will cancel out. Then remember by DeMorgan's law, an OR gate with inverted inputs is a NAND gate. Presto! Four NAND gates.