# Homework Help: Converting AND-OR expression to NAND-NAND?

1. Feb 3, 2010

### Noopi

1. The problem statement, all variables and given/known data
Make a BCD 3321 encoder. So if you input 0100, the encoder will output (depending on your design) either a 1001, or a 0101. Similarly, an input of 0101 will output either a 1010 or a 0110 (again, depending on your design).

2. Relevant equations
I know you're supposed to use DeMorgan's Law, but I have a hard time understanding WHEN to use it.

3. The attempt at a solution
I have done the truth table, the kmaps, and derived the logical expressions for each bit, but what I'm having a hard time doing is turning my AND-OR logic expressions into NAND-NAND logic expressions.

My 4 logical expressions are:

(3) MSB: A + BC
(3) Second MSB: A + B + CD
(2) Third MSB: A + BC'D + B'CD'
(1) LSB: BCD + BC'D' + B'C'D

My professor mentioned something about double negating the equations, and then applying DeMorgan's Law to get the NAND-NAND logic, and that's where he lost me.

Any help will be greatly appreciated!

2. Feb 3, 2010

### Zayer

Keep in mind that in the logic diagram

you will implement it in two-level NAND gate

for example if you have this function f(w,x,y )=xy+xz+w

In the first level you will have (xy)' , (xz)' , w'

Then the second level [(xy)'(xz)'w']'=xy+xz+w