Number Base Converter

What is number base conversion?

Number base conversion changes how a number is represented by changing the base (radix). Decimal (base 10) uses digits 0-9. Binary (base 2) uses only 0 and 1. Octal (base 8) uses 0-7. Hexadecimal (base 16) uses 0-9 and A-F. All represent the same numeric value — just written differently. Example: decimal 255 = binary 11111111 = hex FF.

Why do programmers use hexadecimal?

Hexadecimal (base 16) is compact: one hex digit equals exactly 4 binary bits, so a byte (8 bits) is always two hex digits. This makes memory addresses, color codes (#FF5733), and binary data much shorter. 0xFF is far easier to read than 11111111. Memory addresses and file offsets in debuggers are nearly always shown in hex.

How do I convert binary to decimal?

Multiply each binary digit by 2 raised to its position power (right to left, starting at 0), then sum. Example: 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11. In code: parseInt('1011', 2) in JavaScript, int('1011', 2) in Python, Convert.ToInt32('1011', 2) in C#.

How do I convert decimal to hexadecimal?

Repeatedly divide by 16 and note the remainders. Remainders 10-15 become A-F. Example: 255 ÷ 16 = 15 remainder 15 (F), 15 ÷ 16 = 0 remainder 15 (F). Reading remainders upward: FF. In code: (255).toString(16) in JavaScript gives 'ff', hex(255) in Python gives '0xff'.

What is octal (base 8) used for?

Octal is used primarily in Unix/Linux file permissions. chmod command uses three octal digits: read (4), write (2), execute (1). chmod 755 sets owner as rwx (7=4+2+1), group as r-x (5=4+0+1), others as r-x. Each octal digit maps directly to a 3-bit binary group, making it a compact representation.

How large can numbers be in this converter?

This tool uses JavaScript's Number type which safely handles integers up to 2^53 - 1 (9,007,199,254,740,991 in decimal). For most purposes including 32-bit and 64-bit integers this is sufficient. For cryptographic or arbitrary-precision numbers beyond this range, use JavaScript's BigInt or a dedicated big number library.