I have found a way to memorize the Token-to-ethernet (& back) address conversion - if
you like it, great, if not, ignore it. You probably won't like it unless you really
liked math in school.
So we know that you have to bit-flip each byte, and we know that if each byte is
written as 2 hex digits, then you can swap each pair of hex digits in the byte & flip
each hex digit (example: flipping 7D as a byte is binary 0111 1101 flipped to 1011
1110 which is BE - doing it by the hex digit is 7D swapped to D7, D flips to B & 7
flips to E so it's BE). Now how do you memorize the flip for each hex digit?
THE 1st SIX PRIME NUMBERS (2,3,5,7,11,13) !!!
1st - powers of 2: they are 1,2,4,8 (0 is not a power of 2, it's a multiple; & 16 is
higher than a single hex digit) they flip with each other in high-low pairs, so 1 & 8
flip to each other, & 2 & 4 flip to each other.
2nd - multiples of 3,5,7 (and the 4 magic flips): the multiples of 3 are 0,3,6,9,C
(12), and F (15). 0,6,9 & F are the magic flips - they are the same when flipped(
Remember 4 magic flips for a 4-bit hex digit). The others are 3 & C which flip to each
other. The multiples of 5 are 5 and A (I skipped 0 & F because we already touched them
with the 3's), and they flip to each other. The multiples of 7 are 7 & E, which flip
to each other.
3rd & finally - B (11) and D (13) are all that are left & they flip to each other.
There!
(By the way, for anyone that hasn't fallen asleep yet, the reason for 4 magic flips
isn't because of the 4 digits in a hex number - that's just a mnemonic. Technically,
a magic flip is where you divide the number of digits in half & each half is a mirror
image, so 4 bits divided by 2 is 2, and there are 4 possibilities in a 2-bit number.)
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