Converting a function from AND, NOT and OR gates to just NOR

问题

I have a circuit made from AND NOT and OR gates, i need to convert it so that it only has NOR gates, this isn't working to well for me so any tips would be much appreciated. This is the original function to convert:

~a~b~cd + ~a~bc~d + ~ab~c~d + ~abcd + a~b~c~d + a~bcd + ab~cd + abc~d

回答1:

I'm assuming cd means c AND d. The rules are:

• ~a = a NOR a
• a^b = (a NOR a) NOR (b NOR b)
• a+b = (a NOR b) NOR (a NOR b)

From that, it's purely mechanical. I'll do the first part as an example:

~a~b~cd + ~a~bc~d
(a NOR a)(b NOR b)(c NOR C)d + (a NOR a)(b NOR b)c(d NOR d)
(((a NOR a) NOR (a NOR a)) NOR ((b NOR b) NOR (b NOR b)))(c NOR C)d + (a NOR a)(b NOR b)c(d NOR d)

来源：https://stackoverflow.com/questions/10052492/converting-a-function-from-and-not-and-or-gates-to-just-nor