Task: Draw an AND circuit with 8 inputs, a circuit which implements the expression a∧b∧c∧d∧e∧f∧g∧h.

Condition: Use only NOR-Gates with two inputs to solve this task.

Could anyone give me a hint, what is false here? ( I would like to solve it by my own.)

My suggestion:

enter image description here


My idea was at first to think how can I depict an AND gate with NOR Gates.

Equation: A*B

= (A'+B')'

=> nevertheless A'+B' is A'*B' (using here the Morgans Law) and then adding the inverter to it, it would be (A'B')'. Here the inverters are complements and would cancel each other out, so A * B would be just there

And with this equation I could work with to implement an AND gate, right?


simulate this circuit – Schematic created using CircuitLab

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    \$\begingroup\$ how should this work? your first input stage already only combines inputs with NORs, which aren't XORs, so you obviously lose information right there. \$\endgroup\$ – Marcus Müller May 3 at 22:39
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    \$\begingroup\$ aaaah, OK, you mean \$\wedge\$ as in math, not ^ as in the C and derived programming language! \$\endgroup\$ – Marcus Müller May 3 at 23:04
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    \$\begingroup\$ yeah, but you've got multiple outputs driving the same net (your group of four outputs). That is a very, very, very bad idea. \$\endgroup\$ – Marcus Müller May 3 at 23:04
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    \$\begingroup\$ why do you have groups of two NORs that have the same inputs and drive the same output? That makes absolutely no sense. \$\endgroup\$ – Marcus Müller May 3 at 23:06
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    \$\begingroup\$ This question is qualitatively identical to the one you asked a few days ago, and it doesn't look like you learned anything from the answers to that question. \$\endgroup\$ – Elliot Alderson May 4 at 1:13

I get it that you feel lost in this. But you should be able to do this when almost asleep! Here are some easily verified equivalents. Please check them out and make sure you follow why:


simulate this circuit – Schematic created using CircuitLab

Memorize them, if you need to. They will help you. (There are algebraic ways of saying the same thing, but these graphic equivalents are easier for some to remember.)

All you need to do is to create a 2-input AND gate out of NOR gates. From the above, it's almost trivial to see how to form a 2-input AND gate from NOR gates. And with that, the following is trivially produced:

Now that you know the above, you can work out exactly how to form a 2-input AND gate only from 2-input NOR gates. Assuming you know how to form an 8-input AND gate from 2-input AND gates, the rest should be easy.


simulate this circuit

It's just stamping out the obvious! Really! It's that easy.

Sometimes, once you lay things out like that you may find "optimizations" you can also perform. But that's for another day.

  • \$\begingroup\$ (look at my edit in the question) \$\endgroup\$ – lightsodium May 4 at 13:51
  • \$\begingroup\$ @lightsodium The equation is \$A\cdot B = \overline{\overline{A}+\overline{B}}\$. \$\endgroup\$ – jonk May 4 at 16:57
  • \$\begingroup\$ yes, the second part of the equation was in the next row \$\endgroup\$ – lightsodium May 4 at 17:34
  • \$\begingroup\$ @lightsodium Did you need any further response? Or did I cover what's needed, already? \$\endgroup\$ – jonk May 4 at 17:37
  • \$\begingroup\$ Thanks, I understand it now. \$\endgroup\$ – lightsodium May 4 at 17:51

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