Converters & Math

Conversions that are simple in principle and error-prone by hand: decimal to hex to binary to octal, and the arithmetic that goes with reading a bitmask or a permission flag.

Base conversion comes up more often than its reputation suggests. Unix file permissions are octal because each digit is exactly three bits. Colours, memory addresses and MAC addresses are hex because two digits make one byte. Subnet masks and feature flags only make sense read as binary. The catch is precision: a converter built on ordinary JavaScript numbers goes silently wrong above 2^53, which is well inside the range of a 64-bit database ID, so the tools here use arbitrary-precision integers throughout.

Calendar files belong here too. An .ics is a text format that almost nobody reads by hand, so an invitation that arrives at the wrong time, repeats when it should not, or lists attendees you did not expect is hard to argue with until you can see what the file actually says.

Money compounds here too. What a lump sum or a monthly contribution grows to depends on the compounding frequency, any step-up, and inflation — and the last of those is the one people leave out, which is why a number that looks like a fortune in thirty years often is not.

Borrowing works the other way. Loan offers line up on their true APR once processing fees are counted, a flat rate shows the reducing-balance rate it really is, prepayments show the interest and months they save, and a refinance shows whether, and in which month, it pays for itself.

Pay converts too: an hourly rate into an annual salary, or a salary into what it is a month, twice a month, every two weeks, a week or an hour, with the hours, days and weeks you are paid for — and a second hourly figure once paid holidays are counted, since time off with pay means fewer hours worked for the same money.

And a restaurant bill splits here: evenly or by who had what, with tax and a tip before or after tax, each share rounded up if you like, and the cents handed out so the shares add up to the total exactly.

For students there is the arithmetic of a term: a course grade from weighted marks with its letter, the score a final exam needs for the grade you want, a GPA on the 4-point or the 10-point scale, and a CGPA from each semester turned into a percentage by the formula a board or university sets.

For a salary in India there is gratuity under the labour codes in force since November 2025 — fifteen days’ wages a year on the new wage definition, with its 50% rule, and fixed-term staff paid after one year — and what a CTC comes to in hand after PF, professional tax and income tax under the FY 2026-27 regime.

Before money moves, an IBAN checks here: its check digits, the length and layout its country sets, and the bank’s own check digits where a country has them, with the wrong character pointed out rather than a guessed correction that could be someone else’s account.

A phone number reads here too, against its country’s numbering plan: the country and whether it is a landline, a mobile or toll-free, whether its range is in use, and the same number as E.164, international, national and a tel: link — a whole list of them made consistent for a contacts import.