# Simple Boolean Expression to Circuit

#### goodbyegti

Joined Apr 28, 2004
59
Hi peoples, just thought i'd comment on how great this site is before i start with my question, have had a good read of the boolean algebra section which has been very useful so far, as does the rest of the site. Anyway heres my question:

I've designed a circuit and simplified it using a Karnaugh map and come up with the following after simplifying the minterms:

R = A B C + A B C + A B C + A B C

which i have simplified to:

R = CB + CA

which i hope is correct

(btw sorry for underlines, they should be over the letters.. but i can't figure out how to do it on here)

I now need to design a circuit for this expression using only NAND and NOT gates. I've ages messing around with designs and testing them manually against a truth table and I can't come up with anything that works. To put it simply does anyone have an idea of how i could build this circuit using NAND and NOT gates only? Thanks in advance...

Joined Jan 19, 2004
220
hi
i cant comment on the your simplification of the expression... i am too sleepy to work it out at the moment..so lets assume it to be correct.
for your knowledge any gate can be built using a NAND or NOR gate.. these gates are hence called universal building blocks....
so any logic circuit can be built using them.
you will need:- 1 NAND gate to make a NOT gate
2 NAND gates to make a AND gate
3 NAND gates to make a OR gate.
4 to make a NOR gate.
4 to make a EX-OR gate
5 to make a EX-NOR gate.

with these clues try and work the problem youself...
if you still need help msg back.

#### goodbyegti

Joined Apr 28, 2004
59
thats very useful, thanks a lot, i've got a good idea of what to do now so i'll either figure it out and post up what i think to be the answer or i'll be back asking for more help! thanks again..

#### goodbyegti

Joined Apr 28, 2004
59
Yep, sorted it, thanks for your help, I built a NOR, OR and AND gate from NAND gates like you said and then just used these to build the expression up..thanks again..

#### m4yh3m

Joined Apr 28, 2004
186
Y=A'B'C'+AB'C'+AB'C+ABC

Simplified:
Y=B'C'+AC