05 // Unicode, Symbol & Encoding WorkbenchNUMBER-BASE-BITWISE
Binary, Hexadecimal, Decimal & Octal Programmer Workbench
Converts arbitrary-precision integers cleanly across radix 2, 8, 10, and 16 using native `BigInt` arithmetic so 64-bit registers and memory addresses never lose precision above `2⁵³ − 1`.
DECIMAL (10)
255
HEX (16)
0xFF
BINARY (2)
0b11111111
OCTAL (8)
0o377
A & B
15 (0xF)
A | B
255 (0xFF)
A ^ B
240 (0xF0)
A << 1 / A >> 1
510 / 127
Was this tool helpful?
Reference Table
- 01JavaScript `Number.MAX_SAFE_INTEGER` is `9,007,199,254,740,991` (`2⁵³ − 1`); using `BigInt` preserves exact bit accuracy for 64-bit and 128-bit unsigned integers.
- 02Each hexadecimal digit maps 1-to-1 onto an exact 4-bit binary nibble (`0x0 = 0000` through `0xF = 1111`).
Frequently Asked Questions
Why do systems programmers prefer hexadecimal over decimal?+
Because 1 hex digit equals exactly 4 bits and 2 hex digits equal 1 byte (`0x00–0xFF`), aligning cleanly with byte boundaries and memory page sizes.
Where is octal (base 8) still used today?+
POSIX/Linux `chmod` file permission masks (e.g., `0755` = `rwxr-xr-x`, where each octal digit encodes 3 permission bits `rwx`).
How are negative integers represented in binary hardware?+
Almost universally via Two's Complement: invert all bits (`~x`) and add `1`, so `-1` in 8-bit signed binary is `11111111` (`0xFF`).