# hpr1292 :: Doomsday Remainders

### Reflections on remainders inspired by Doomsday Rule sign-off. Applications to programming and arithm

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arithmetic, remainder, mod. (Be the first).
The show is available on the Internet Archive at: https://archive.org/details/hpr1292

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Duration: 00:34:42

### Part of the series:general.

```Last Episode on Conway's Doomsday Rule ends with teaser on MOD(), a
"remainder" function defined for integer values (whole numbers):

MOD(K, m) = remainder when K is divided by "modulus" m.

Examples:
a. MOD(207, 7) = MOD(207 - 140, 7) = MOD(67, 7) = 4
b. MOD(1234567, 2) = 1 because the number is odd

MOD() function found in most spreadsheet programs, but it also shows up
as an operator in some programming languages: (a % b), or (a mod b).

Other functions referenced:
DIV(K, m)    = quotient in integer division
where K = m * quotient + remainder (not returned)
0 <= remainder < m

DIVMOD(K, m) = (quotient, remainder) when K is divided by m
where remainder = MOD(K, m)
quotient  = DIV(K, m)
K = m * quotient + remainder
```

## Show Transcript

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