Rakesh Sharma said:
Hi,
How would I construct an XOR function using NOR gates ONLY? I have
tried breaking my head over it but haven't come up with a solution.
Thanks in advance
Rakesh
All of the propositional functions can be expressed in terms of 'nor',
(or in terms of 'nand')
If 'nor' is primitive:
1. not(p) =df (p nor p)
2. (p or q) =df not(p nor q)
3. (p and q) =df not(not(p) or not(q))
4. (p nand q) =df not(p and q)
5. (p only if q) =df (not(p) or q)
6. (p if q) =df (p or not(q))
7. (p if and only if q) =df (p if q) and (p only if q)
8. (p xor q) =df not(p if and only if q).
1a. ~p <-> (p nor p)
2a. (p v q) <-> ~(p nor q)
3a. (p & q) <-> ~(~p v ~q)
4a. (p nand q) <-> ~(p & q)
5a. (p -> q) <-> (~p v q)
6a. (p <- q) <-> (p v ~q)
7a. (p <-> q) <-> ((p <- q) & (p -> q))
8a. (p xor q) <-> ~(p <-> q).
etc.