Re: How to construct XOR function using NORs?

From: Witt (oorionus_at_yahoo.com)
Date: 09/29/04 

Date: Wed, 29 Sep 2004 13:53:31 -0400

    "Rakesh Sharma" <srakesh@hotmail.com> wrote in message
  news:17c0a468.0409261152.eb042ba@posting.google.com...
> 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.

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