Hex Numeral XOR and Bit-Reversal Tables

XOR TABLE
XOR 0 1 2 3 4 5 6 7 8 9 A B C D E F
0 0 1 2 3 4 5 6 7 8 9 A B C D E F
1 1 0 3 2 5 4 7 6 9 8 B A D C F E
2 2 3 0 1 6 7 4 5 A B 8 9 E F C D
3 3 2 1 0 7 6 5 4 B A 9 8 F E D C
4 4 5 6 7 0 1 2 3 C D E F 8 9 A B
5 5 4 7 6 1 0 3 2 D C F E 9 8 B A
6 6 7 4 5 2 3 0 1 E F C D A B 8 9
7 7 6 5 4 3 2 1 0 F E D C B A 9 8
8 8 9 A B C D E F 0 1 2 3 4 5 6 7
9 9 8 B A D C F E 1 0 3 2 5 4 7 6
A A B 8 9 E F C D 2 3 0 1 6 7 4 5
B B A 9 8 F E D C 3 2 1 0 7 6 5 4
C C D E F 8 9 A B 4 5 6 7 0 1 2 3
D D C F E 9 8 B A 5 4 7 6 1 0 3 2
E E F C D A B 8 9 6 7 4 5 2 3 0 1
F F E D C B A 9 8 7 6 5 4 3 2 1 0
 
4-BIT-REVERSAL
NIBBLE REV
0 0
1 8
2 4
3 C
4 2
5 A
6 6
7 E
8 1
9 9
A 5
B D
C 3
D B
E 7
F F


Worked example :-
XOR the string "FEE" and then bit-reverse the odd-position numeral.
Solution - break the string down into numeral pairs - "FE" = 1, "EE"=0 so XOR result is "10", then bit-reverse 1 - being "8", so final result
is "80".

Hints:- Ignore the start and stop sentinals - "D". If the first number after the start sentinal is odd, XOR the whole string of numerals then
bit-reverse all odd position numerals, if even, XOR the whole string then bit-reverse all the even position numerals. Remember 0, 6, 9
and F stay the same on bit-reversal.

You can also use Microsoft Excel to do automated XOR calculations on a numeral by numeral basis (as it can't handle 48 numeral strings).
You will need to install the Analysis Toolkit Add-In. For earlier versions of Excel you need to use VBA to create the "BITXOR" function.

To do this open VBA, create a new Module and enter the following function:-
"Public Function BITXOR(x As Long, y As Long)
BITXOR = x Xor y
End Function"

Then use the following formula in each Nibble Result Cell
"=DEC2HEX(BITXOR(HEX2DEC(SourceNibbleCell1),HEX2DEC(SourceNibbleCell2)))".