[H-GEN] Mysql & bitwise xor

[W. Sierke]

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"Raymond Smith" wrote:
> To the original poster: if you have 'and', 'or', and 'not' you
> can usually do everything you need. A quick search on Google for
> 'intro boolean logic' should bring up useful starting resources.
> When starting out, Truth Tables are your friend.

In fact only 'not' and one of either 'and' or 'or' are required: both 'and'
and 'or' can be constructed from the other when suitably combined with
'not'.

Consider the lily:

W =  A  or   B
X =  A  and  B
Y = ~A  or  ~B
Z = ~A  and ~B

| A  B | W  X | |~A ~B | Y  Z |
|------+------| |------+------|
| 0  0 | 0  0 | | 1  1 | 1  1 |
| 0  1 | 1  0 | | 1  0 | 1  0 |
| 1  0 | 1  0 | | 0  1 | 1  0 |
| 1  1 | 1  1 | | 0  0 | 0  0 |

Looking at the first (W, X) table, notice the symmetry for W and X, that is
X looks like W, but upside down (implying negation of the source operands)
and inverted (implying negation of the result - c.f. (Y, Z) ). Indeed by
comparing the tables for the 'or' (W, Y) and 'and' (X, Z) operations, we see
how either set in isolation is capable of producing equivalent results.
Again, a beautiful symmetry is evident (well, I guess it's like art, you
either get it or you don't). This also demonstrates that there are two ways
to achieve the same result - compare X and ~Y for an example (remembering
that X is an 'and' operation and Y is 'or').

| A  B ~A ~B | W ~W  Y ~Y | X ~X  Z ~Z |
|------------+------------+------------|
| 0  0  1  1 | 0  1  1  0 | 0  1  1  0 |
| 0  1  1  0 | 1  0  1  0 | 0  1  0  1 |
| 1  0  0  1 | 1  0  1  0 | 0  1  0  1 |
| 1  1  0  0 | 1  0  0  1 | 1  0  0  1 |


Wayne


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