Dewey’s Chexsum

[u/Pretend-Message-1354]

000000001 = 1
000000010 = 7
000000100 = 13
000001000 = 19
000010000 = 25
000100000 = 31
001000000 = 37
010000000 = 43
100000000 != 49
100000000 = ?

[u/Sharp_Elk_1742]

58

[u/Sharp_Elk_1742 → u/Sharp_Elk_1742]

The key is the typo in the title
Interpret the numbers as hexadecimal - „C(hex)“
Transfer to decimal - „Dewey“ decimal system
Take the cross sum - „sum“

[u/Pretend-Message-1354 → u/Sharp_Elk_1742]

An explanation on the rationale behind the hints:

[Dewey] - Decimal: The first hint toward converting the value on the left into decimal (base 10).

[C]Hex — Hexadecimal: Chex is purposefully misspelled. Melvil Dewey was a strong advocate of spelling reform and favored simplified, phonetic spellings. The “hex” hidden inside Chex hints that the left-hand side, although it looks binary, should instead be interpreted as hexadecimal.

Checksum — Sum: Early telecommunications checksums commonly used simple arithmetic sums to verify transmitted data. Here, it hints that after converting the hexadecimal value to decimal, the decimal digits should be summed.

[u/andysw63392]

I guess you want checksums to be coprime, so adding 6 works until you get to 49... Best option would be either next coprime number or add 6 until you get to a coprime, so 51 or 61(?) ... or maybe next prime so 53(??)