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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.

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  • \$\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
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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}\$.

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  • \$\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

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