Converting logic circuit to using only 2-input NAND gates and NOT gate

[colerelm]

Homework Statement

Convert the logic circuit to an equivalent circuit constructed from 2-input NAND gates and NOT gates.
http://imgur.com/EzOBdbv

Homework Equations

Pretty sure the boolean equation is:
A & (~(~B+C)+~D + E)

The Attempt at a Solution

I know for sure that ~A + ~B = ~AB so I was trying to add an inverter to the input of each OR gate to try to make use of this equation but I get stuck at the spot where I need to convert a 3-input OR gate to a two input NAND gate. Can anyone please help?

 

[NascentOxygen]

Hi colerelm, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

A & (~(~B+C)+~D + E)

You need to convert all the OR operations to AND/NAND. It is usually best to do this as Boolean algebra, rather than piece by piece in the logic gates diagram. The latter may not be simplest, and it's difficult to spot redundancy. (EDIT: why not try it both ways, and see whether they give the same result here?)

Q: How to fabricate a 3-input NAND gate using 2-input NAND gates? Can you do that?