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.