Number bases

Packages: ARITHMETIC_PACKAGE, FUNCTION_PACKAGE, CONVERTERS_PACKAGE, UOM_PACKAGE, BIGINT_PACKAGE. Registered by createEngine(); for a slimmer engine, register them explicitly (see choosing packages).

A base is the number of distinct digits a number is written with: everyday decimal has ten, hexadecimal has sixteen, binary two, octal eight. The same value can be written in any of them, mixed freely with ordinary decimals, and shown back in whichever base you want.

Writing a number in another base

0xFF // 255
0b1010 // 10
0o17 // 15
0xDEADBEEF // 3,735,928,559

The prefix is case-insensitive and so are hex digits, so 0XFF, 0xff and 0xFF are the same number.

0xff // 255
0XFF // 255

A literal in any base is just a number, so bases mix in one expression and the result comes back in decimal.

0xFF + 0b1010 + 0o17 // 280
0x1F + 1 // 32

Showing a number in another base

as converts the display, and there is a function form for each base.

255 as hex // 0xFF
255 as binary // 0b11111111
255 as octal // 0o377
hex(4095) // 0xFFF
hex(255) // 0xFF
bin(10) // 0b1010
bin(5) // 0b101

int goes the other way, though a literal is already a number so it is rarely needed.

int(0xFF) // 255

A base is still a number

Converting a number to another base changes how it is written, not what it is, so the result keeps doing arithmetic.

hex(255) + 1 // 256
(255 as binary) + 1 // 256
~hex(255) // -256

A negative keeps its sign outside the literal, and a fraction is truncated, since there is no useful way to write a fractional hex digit.

hex(-255) // -0xFF
255.7 as hex // 0xFF