mixradix

Add, subtract and convert integers of any size in mixed radix bases, where every digit position has its own radix: hours:minutes:seconds, pounds:shillings:pence, feet:inches, or plain hexadecimal. Zero dependencies, fully typed, with a command line tool.

pipx install mixradix        # or: pip install mixradix / uv tool install mixradix

$ mixradix add 23:59:59 1 -b 24:60:60
1:0:0:0
$ mixradix sub 0:15 0:30 -b 24:60/wrap
23:45
$ mixradix convert 100000 -t 24:60:60
1:3:46:40

Also available for JavaScript and TypeScript as mixradix on npm, with the same behaviour and CLI.

Bases

A base lists one radix per digit position, most significant first, like the digits of a number:

The part after / is the overflow: what happens left of the leftmost radix.

So 30 days in 24:60:60 is 30:0:0:0, and in 24:60:60/wrap it is 0:0:0.

Numbers

• One character per digit (ff, 1011, case-insensitive) in a base with one radix of at most 36, like 16 or 2.
• Decimal digits separated by : (1:23:59) in every base.
• In a base like 24:60:60, text without : is a single digit: 45 is 45 seconds.
• A leading - or + sets the sign. With wrap, values are never negative.

Every digit must be below its position's radix, so 1:60:0 is rejected in 24:60:60.

Command line

mixradix add <NUMBER> <NUMBER>... [-b BASE] [-t TO] [--json]
mixradix sub <NUMBER> <NUMBER>... [-b BASE] [-t TO] [--json]   (alias: subtract)
mixradix convert <NUMBER> -t TO [-b BASE] [--json]
mixradix info <BASE> [--json]

• -b, --base: the base the numbers are written in. Defaults to 10.
• -t, --to: the base to write the result in. Defaults to --base.
• Negative numbers work as they are: -5, -1:30, -ff. Only one that starts with an option letter, like -b1 in base 16, goes after --.

$ mixradix add 1:30 2:45 0:50 -b 60                  # sum of durations
5:5
$ mixradix add 1:19:11 1 -b 20:12                    # pounds:shillings:pence
2:0:0
$ mixradix convert ff -b 16 -t 2
11111111
$ mixradix convert -90 -t 60 --json
{"result":"-1:30","value":-90,"digits":[1,30],"negative":true,"base":"60"}
$ mixradix info 24:60/wrap
base:         24:60/wrap
overflow:     wrap (values wrap around modulo 1440)
digits:       exactly 2
place values: 60, 1
range:        0 to 1439

Exit codes: 0 on success, 1 for an invalid base or number, 2 for a usage error. python -m mixradix works too.

Library

from mixradix import MixedRadix, MixedRadixNumber, add, sub, convert

# Quick string in, string out.
add("23:59:59", "1", base="24:60:60")        # '1:0:0:0'
sub("1:0:0", "1", base="24:60:60", to=10)    # '3599'
convert(5000, to="24:60:60")                 # '1:23:20'

# Bases and numbers.
time = MixedRadix("24:60:60")                # or MixedRadix([24, 60, 60])
t = time.parse("1:23:59")                    # or time.from_int(5039)
t.value, t.digits                            # 5039, (1, 23, 59)
str(t + 1), str(t - "0:23:59")               # '1:24:0', '1:0:0'
str(t.to(10))                                # '5039'
t == 5039                                    # True: comparison is by value

clock = MixedRadix([24, 60], overflow="wrap")
str(clock.parse("23:30") + "1:0")            # '0:30'

MixedRadixNumber("ff", 16).value             # 255

Operands can be other numbers in any base, ints, or text in the left operand's base. The result uses the left operand's base.

Errors are MixedRadixError (a ValueError) with subclasses InvalidBaseError, InvalidNumberError and DigitOutOfRangeError.

License

MIT OR Apache-2.0, at your option.