Boolean Algebra, using DeMorgan's law

Question

I have obtained this function:

$$(\overline{A}*D) + (\overline{A}*C) + (\overline{B}*\overline{D})$$

... after I have used Karnaugh Map to simplify the canonical expression.

And now, I am needing to get and equivalent expression using DeMorgan's law to implement the function with NAND gates.

So I have followed these steps:

1º

$$(\overline{A}*D) + (\overline{A}*C) + (\overline{B}*\overline{D})$$

2º

$$\overline{\overline{(\overline{A}*D) + (\overline{A}*C) + (\overline{B}*\overline{D})}}$$

3º

$$\overline{(\overline{\overline{A}*D}) * (\overline{{\overline{A}*C}}) * (\overline{\overline{B}*\overline{D}}})$$

But it is not an equivalent function... thus what I have done wrong?

Answer 1

It is equivalent, but I had been implementing the function of wrong way.