# Modify boolean equation to get 3 input NOR equation using boolean algebra rules

I was taking a look at this link http://lizarum.com/assignments/boolean_algebra/chapter3.html to try and solve an equation I have. The original equation is:

H = MC + MC' + CRD + M'CD'

I simplified it to H = M + CRD + M'CD'

Here is my attempt:

H = ((M + CRD + M'CD')')'
H = ((M)' * (CRD)' * (M'CD')')'
H = (((M)')' + ((CRD)')' + ((M'CD')')'
H = ((M')' + (C'+ R' + D')' + (M + C' + D)')'


Is that final equation a 3 input NOR equation? I have a feeling that I'm missing a step that makes the first parentheses into three variables.

EDIT: Since I need 3 variables in the final NOR expression can I take the original and expand as such?

 H = MC + MC' + CRD + M'CD'
H = MC(1) + MC'(1) + CRD + M'CD'
H = MC(D + D') + MC'(D + D') + CRD + M'CD'
H = MCD + MCD' + MC'D + MC'D + CRD + M'CD'


and then get the 3 input NOR from the following:

 H = ((MCD + MCD' + MC'D + MC'D' + M'CD' + CRD)')'
H = ((MCD)' * (MCD')' * (MC'D)' * (MC'D')' * (M'CD')' * (CRD)')'
H = (((MCD)')' * ((MCD')')' * ((MC'D)')' * ((MC'D')')' * ((M'CD')')' * ((CRD)')')'
H = (M'+C'+D')' + (M'+C'+D)' + (M'+C+D')' + (M'+C+D)' + (M+C'+D)' + (C'+R'+D')'


I'm inclined to believe the final equation should be of this form above. Please let me know if this looks correct. But this would mean that the final NOR gate has 6 inputs which is not good -_-

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