Hex calculator

Type a sum the way you'd write it: `1A3F + FF`, `100 - 1`, `FF * 2`, `FF / 10`. The answer comes back in hex, decimal and binary, each with a copy button, and the working shows how it was done.

Besides + − × and ÷, it understands `mod`, `AND`, `OR`, `XOR`, `NOT`, the shifts `<<`, `>>` and `>>>`, and `ROL` and `ROR` for rotating. Letters can be either case, and `0x1F` or `1Fh` both mean hex 1F. To mix in a decimal or binary number, change Numbers are in.

It works exactly like decimal addition, except that a column carries when it reaches 16, not 10. In `1A3F + FF`, F + F is 30 in decimal, which is 1E in hex, so write E and carry 1. Then 3 + F + 1 is 19, which is 13 in hex, so write 3 and carry 1. A + 1 is B, and the 1 at the front comes down. The answer is 1B3E.

The working writes the carries above the columns, so you can check each one. It helps to know the digits past 9 by heart. A is 10, B 11, C 12, D 13, E 14 and F 15.

Subtraction borrows 16 from the next column when the top digit is too small. In `100 − 1` the first two columns both have to borrow, which is why the answer is FF, and the working marks each borrow with a b. If the second number is bigger, the answer is negative, and the calculator also gives its two's complement, which is how a computer stores it.

Multiplication and division are worked through decimal, which is how most people check them by hand. Division is whole-number division, as in programming languages, with the remainder given separately: `FF / 10` is F remainder F.

Programmers like hex numbers that spell words. Every Java class file starts with the four bytes CA FE BA BE, chosen as a nod to the baristas at Peet's Coffee & Tea. 0xDEADBEEF was used on IBM RS/6000 systems and on PowerPC Macs to mark memory that hadn't been set yet, so a crash dump full of it was easy to spot. Both work because hex digits include six letters, and words built from A to F are rare enough to stand out.