# NAND gates help

Discussion in 'Electronics Homework Help' started by NanyBany, Jun 30, 2014.

1. ### NanyBany

12
0
May 15, 2014
This is my Boolean expression: B!C + AC

I would like to know how I can make this circuit using NAND gates only. Any help is appreciated. Thank you.

2. ### (*steve*)¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥdModerator

25,387
2,772
Jan 21, 2010
Hi NanyBany. I've moved your thread to the homework section, because I believe that's what it is.

you might like to try factoring the equation first (it's optional, but it looks like it would lead to a simpler result.

Then, I assume you've done enough Boolean algebra to know how to convert an AND to an OR, and vice versa. I also assume you know how to invert a logic state using the NAND function.

Armed with this knowledge you can directly implement the logic function.

The final step (again optional) is to simplify the resulting gates. Can you think of one obvious simplification already?

KrisBlueNZ likes this.
3. ### Laplace

1,252
184
Apr 4, 2010
Forget about working with Boolean equations to solve this except for realizing that an AND gate with negated output is equivalent to an OR gate with negated inputs, and that an OR gate with negated output is equivalent to an AND gate with negated inputs.

So just draw the logic diagram with AND, OR, & inverter gates. Then add double inversion circles to any signal line so that AND gates have a negated output and the OR gates have a negated input -- both are equivalent to NAND gates. The logic function in question can be implemented with 4 NAND gates (one used as an inverter).  