Why the ASCII value of a digit character is equal to the value plus ‘0’?

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Because the integral values of the digit characters are guaranteed by the C standard to be consecutive.

Therefore '1' - '0' == 1, '2' - '0' == 2, etc. from which you can infer that your formulas really do work.

Sidenotes:

  1. Since this is guaranteed by the standard, it works even if the target platform does not use ASCII.
  2. Conversely, if the standard did not mandate this (it does not do so with the values of the letters) then this technique would not be portable; it would be dependent on the target system using ASCII.

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