# Converting Four Variable OR to NOR (using only NOR GATE)

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:

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

• what do you mean by OR(OR(A,B,C,D)) ? – Ahmad Bazzi Apr 12 at 9:51
• @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. – amir na Apr 12 at 9:59

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 $$A\vee B\vee C \vee D = \overline{\overline {A\vee B\vee C \vee D}\vee \overline{A\vee B\vee C \vee D}}$$