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I want to convert a four variable OR (i.e. OR(A,B,C,D)) to NOR. I did this using 6 two variable NOR like the picture below. but I think it can be done easier. Can anyone suggest any way to do this and avoid using this amount of gates. For example using a 4 variable NOR instead of this 2 variable NORs.

Actually I did this:

$OR(A,B,C,D) = OR(OR (A,B) , OR(C,D)) = NOT(NOR(NOT(NOR(A,B)) , NOT(NOR(C,D)))$

enter image description here

enter image description here

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  • $\begingroup$ what do you mean by OR(OR(A,B,C,D)) ? $\endgroup$ – Ahmad Bazzi Apr 12 at 9:51
  • $\begingroup$ @AhmadBazzi OH. By 4 Variable or, I mean OR(A,B,C,D). I think I forgot an (i.e.) there and it led to misunderstanding. Sorry. $\endgroup$ – amir na Apr 12 at 9:59
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Apply $Q=\overline{\overline{Q} \vee \overline{Q}}.$
In the present case, with the use of two $4-$inputs NORs and one $2-$inputs NOR you have $$A\vee B\vee C \vee D = \overline{\overline {A\vee B\vee C \vee D}\vee \overline{A\vee B\vee C \vee D}}$$

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