Convert numbers between binary, octal, decimal and hexadecimal — all four fields update as you type.
Every number has one value and many representations. Decimal 255 is 11111111 in binary, 377 in octal and FF in hexadecimal — the same quantity written with different alphabet sizes. Programmers move between these bases constantly: binary exposes the individual bits behind flags and masks, hexadecimal compresses those bits into pairs of digits (FF = 8 bits set), and octal survives in Unix file permissions like 755.
The conversion rule is positional: each digit is multiplied by the base raised to its position. In binary, 1011 is 1×8 + 0×4 + 1×2 + 1×1 = 11. Going the other way, you divide repeatedly by the target base and read the remainders backwards. This converter does both directions live, validating that each field only contains digits that exist in its base — typing a 9 in the octal field or a G in hex flags the input instead of guessing.
Hexadecimal deserves its ubiquity because one hex digit is exactly four bits: two hex digits describe a byte, six describe an RGB color (#0088FF), and memory addresses read compactly. Once that 4-bit mapping clicks, converting between binary and hex can be done by eye — this tool is the shortcut while it does.
Positional notation: a number dₙ…d₂d₁d₀ in base b equals Σ dᵢ × bⁱ. To convert decimal → base b, divide repeatedly by b and read the remainders from last to first.
Base 16 needs sixteen symbols and we only have ten digits — A through F represent the values 10 through 15.
Mainly Unix/Linux file permissions: 755 means rwxr-xr-x, each octal digit encoding three permission bits.
Integers up to the JavaScript safe limit (2⁵³ − 1, about 9 quadrillion). Beyond that, precision would be lost, so the field warns instead.
The tool covers non-negative integers, which is the everyday case in programming. Fractional conversion uses a different expansion and two's complement depends on a fixed bit width.
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