I have this initial function \begin{split}(\overline{A}+\overline{B})(\overline{D}+\overline{C})+AB\overline{(\overline{C}+\overline{D})}\end{split} Which i reduced to \begin{split}{\overline{AB}*\overline{CD}}+ABCD \end{split} The first part is easy to do with NAND but the OR ABCD part i have no ideia how to do...I suspect thats where the XOR comes in and i maybe shouldn't have reduced so much the function.

  • $\begingroup$ You can express everything just with NANDs. $\endgroup$ Dec 30, 2017 at 10:29

1 Answer 1


I have assumed that only 2 input NAND gates are available.

For $\overline {AB}*\overline {CD}$

Take A and B as input and feed them to a NAND gate. U will get $\overline {AB}$. Similarly u can get $\overline {CD}$.

Now feed $\overline {AB}$ and $\overline {CD}$ as input to another NAND gate . U will get AB + CD using demorgan law.

For ABCD take $\overline {AB}$ and complement it using a NAND gate to get AB. Take $\overline {CD}$ and complement it to get CD. Now feed AB and CD to NAND gate. You will get $\overline {ABCD}$.

Now feed (AB+CD) and (ABCD)' to NAND gate. U will get $\overline{(AB+CD)\overline{(ABCD})}$.Apply demorgan law. U have ur answer.

The trick is to express the function as a sum of products which u already have. Now derive the complement of each product term. When all product terms have been derived then feed then to a NAND gate. This final NAND gate will complement the already complemented product terms and add them thus giving the desired answer.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.