Version 6 of ^

expr bit-wise "xor" operator

Arguments must be integers, result is an integer.

Bit n of the result is 1 if bit n of the two arguments differ. Otherwise, bit n of the result is 0.

To evaluate $a^$b when either $a or $b is negative, we make use of the following reasoning:

 | $a>=0, $b>=0 | Bitwise operation |
 | $a>=0, $b<0  | $a^$b == ~($a ^ ~$b)        Contrapositive law |
 |              |       == ~($a ^ (-1-$b))    Extended definition of [~] |
 |              |       == -1-~($a ^ (-1-$b)) Extended definition of [~] |
 |              | Since $a and (-1-$b) are both positive, the [^] in the |
 |              | last expression can be evaluated in bitwise fashion |
 | $a<0, $b>=0  | Commute to ($b^$a) and evaluate as above. |
 | $a<0, $b<0   | $a^$b == (~$a) ^ (~$b)     Contrapositive law |
 |              |       == (-1-$a) ^ (-1-$b) Extended definition of [~] |
 |              | Since (-1-$a) and (-1-$b) are both positive, the [^] |
 |              | in the last expression can be evaluated in bitwise |
 |              | fashion. |%

Examples

% expr 0b010 | 0b000
2

[So, what do I need to add to this example so the result is binary as well? Some sort of format - but I don't see a binary conversion sequence in the docs...]