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XOR tables with zeroes
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Posted on: Tue Aug 28, 2018 6:02 am

Posts: 75
Joined: Tue Apr 24, 2012 7:47 pm
XOR tables with zeroes
Good morning to everybody here on calcudoku.org. In the interest of helping you guys solve the bitwise puzzles in Advanced Calcudoku volume IV, I've decided to post XOR tables with zeroes. XOR is the "exclusive or" operator which works like this:

0 and 1 make 1
0 and 0 make 0
1 and 1 make 0

Imagine that we wanted to combine the numbers 1 and 2 with XOR.

1.......0001
2.......0010

Following the rules above, we get a final result of 0011 which equals 3 in the decimal system.

Now suppose we had a 3-cell XOR cage containing the digits 1, 2, and 3. How exactly would that work?

1.......0001
2.......0010
3.......0011

The XOR operator takes binary strings 2 at a time, so we'll need to use an intermediate result for this calculation.

As shown in the 2-cell example above, adding 1 and 2 gives a result of 0011. Now we're going to take that intermediate result of 0011 and add the binary representation of 3 to it like so.....

intermediate result is 0011
"3" written in binary is 0011

Working from left to right, we get a final answer of 0000 which of course equals 0 in the decimal system.

Having given a brief explanation and examples, I now present my XOR tables.

2 cell table

1: 01 23 45 67
2: 02 13 46 57
3: 03 12 47 56
4: 04 15 26 37
5: 05 14 27 36
6: 06 17 24 35
7: 07 16 25 34
8: 08
9: 18
10: 28
11: 38
12: 48
13: 58
14: 68
15: 78

3 cell table

0: 011 022 033 044 055 066 077 088 123 145 167 246 257 347 356
1: 001 023 045 067 122 133 144 155 166 177 188 247 256 346 357
2: 002 013 046 057 112 147 156 233 244 255 266 277 288 345 367
3: 003 012 047 056 113 146 157 223 245 267 344 355 366 377 388
4: 004 015 026 037 114 127 136 224 235 334 455 466 477 488 567
5: 005 014 027 036 115 126 137 225 234 335 445 467 566 577 588
6: 006 017 024 035 116 125 134 226 237 336 446 457 556 677 688
7: 007 016 025 034 117 124 135 227 236 337 447 456 557 667 788
8: 008 118 228 338 448 558 668 778
9: 018 238 458 678
10: 028 138 468 578
11: 038 128 478 568
12: 048 158 268 378
13: 058 148 278 368
14: 068 178 248 358
15: 078 168 258 348

I did NOT differentiate between L-shaped and in-line 3-cell cages in the tables above. Even if you guys don't see any XOR operators in Advanced Calcudoku volume IV, this post may very well inspire Patrick to include it in subsequent volumes. And if you DO have to tussle with XOR, now you've got tables to help you out! As always, it's my pleasure making these tables for you guys and best of luck with Advanced Calcudoku volume IV.

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