I've been trying to work on a few problems, though I'm not sure how to rewrite this a few circuits using only NAND/NOR -->

an example is shown below;

enter image description here

How am I able to rewrite only using NAND + NOR gates if anyone is able to help me on this.

Thank you.

  • \$\begingroup\$ Hint: if you put bubbles on both ends of a wire, it doesn't change the circuit function. \$\endgroup\$ – The Photon Jan 10 at 6:21
  • \$\begingroup\$ @The Photon I'm sorry, I posted the wrong problem. I had already done that one earlier by reduction I will update the picture now \$\endgroup\$ – user209499 Jan 10 at 6:24
  • \$\begingroup\$ OK, you should still be able to solve this using the rules in my answer. \$\endgroup\$ – The Photon Jan 10 at 17:51

Three hints that can solve this:

  1. You can implement an inverter by either a NAND or a NOR gate with both inputs connected to the same signal.

  2. You can put bubbles on both ends of a wire without changing the circuit function.

  3. An AND gate with both inputs inverted is equivalent to a NOR gate, and an OR gate with both inputs inverted is equivalent to a NAND gate. Graphically, this can be thought of as "pushing the bubbles through" the gate, leaving one bubble on the output and changing the type of gate. Or, in symbols \$\bar{A}\bar{B} =\overline{A+B}\$.

  • \$\begingroup\$ @user209499 ThePhoton's point 3 is commonly called DeMorgan's Theorem. You should get to know it well. \$\endgroup\$ – Elliot Alderson Jan 10 at 13:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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