Semiconductor & Computer Engineering
$xor returns the binary XOR of 2 numbers.
Synopsis[edit]
$xor(<N1>,<N2>)
Parameters[edit]
- N1,N2 = the numbers, in base10/decimal
Note: Fractions are ignored. valid range is integers from -(2^32-1) through +(2^32-1). Negative numbers within that range are translated from signed 32bit-int to unsigned 32bit-int. i.e. Negative numbers in the range -4294967295 through -1 are replaced by N+4294967296. Numbers outside that range are replaced by the closest valid number. i.e. 4294967296+ is handled as if it's 4294967295, and -4294967296 and lower are handled as if -4294967295 which is then handled as if -4294967295+4294967296=1. This means the result is always in the range 0 thru +4294967295.
Properties[edit]
None
Example[edit]
XOR is "Exclusive OR" comparison of a pair of bits. For each bit position it returns 0 if BOTH or NEITHER bits are 1, and returns 1 if exactly 1 of the pair is a 1-bit. In effect, every 1-bit in the 2nd number toggles the 0/1 state of the corresponding bit of the 1st number
//echo -a $xor(21,9) ; returns 28
Here's how the answer was calculated:
- If either number is below -4294967295 replace it with -4294967295
- If either number is above +4294967295 replace it with +4294967295
- If either number is below zero, add 4294967296 to bring it into range of 0 through 4294967295
- Convert each number to binary, then line them up vertically so there are 2 rows, where each position pair is a single column.
- Create a 3rd row, where each column's 0 or 1 value is the XOR of the bit pair directly above it
- Convert the 3rd row from binary to base 10.
//echo -a $base(21,10,2,8) | echo -a $base(9,10,2,8) | echo -a $str(-,8) | echo -a $base($xor(21,9),10,2,8) ; returns: 00010101 00001001 -------- 00011100
The columns where both numbers are zero remain 0. The columns where only 1 of the 2 values is 1, and the column where both values were 1 is zero.
$xor then returns the answer in base 10. Depending on which bits have changed to 0 or 1, the answer can be less than or greater than the 2 numbers:
//echo -a $base(00011100,2,10) ; returns 28
//echo -a $xor(-1,0)
- returns 4294967295 because -1 was translated to 4294967295 in a preliminary step. Then, the XOR of all numbers in the valid range against 0 is the same number.
//echo -a $xor(4444444444,5555555555)
- returns 0. Both numbers were outside valid range, so both were replaced with 2^32-1, and XOR of the same number against itself is always zero.
//var %a $and(%a,1) | var %b $and(%b,1) | if ($xor(%a,%b)) goto label
- Goes to label only if exactly 1 of the 2 variables is 1
//echo -a $xor($pi,2.777777)
- result is 1, because both fractions are ignored.
//echo -a $xor(1,2) = 3 and $xor(-1,-2) is same as $xor(4294967295,4294967294)
//echo -a $xor(-9999999999,0) Invalid negative number replaced with -4294967295, which is replaced with +1. Result is 1.
Compatibility[edit]
Added: mIRC v5.61
Added on: 23 Sep 1999
Note: Unless otherwise stated, this was the date of original functionality.
Further enhancements may have been made in later versions.