Number base converter

In base 10 each digit position is worth ten times the one to its right: 255 = 2 × 100 + 5 × 10 + 5 × 1. Other bases work the same way with a different multiplier. In binary (base 2) the positions are worth 1, 2, 4, 8, 16 and so on, so 11111111 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. In hexadecimal (base 16) they're worth 1, 16, 256, 4,096…, and the digits 10 to 15 are written A to F, so FF = 15 × 16 + 15 = 255.

• Binary is how computers store data. Each digit is a bit; eight bits make a byte.
• Hexadecimal is a compact way to write binary: one hex digit is exactly four bits. You'll see it in HTML colors (#FF8800), memory addresses, MAC addresses and error codes.
• Octal groups bits in threes and survives mainly in Unix file permissions (chmod 755).
• Base 36 uses all digits and letters and is used for short IDs and URL shorteners.

The result shows binary in groups of four and hex in groups of two, which makes long values easier to read and copy. The copy button copies the plain digits without spaces.

The converter works with whole numbers of any length, not just the 64-bit range of a typical calculator, so you can convert a 40-digit decimal number or a 256-bit hex key exactly. The 0x prefix for hex and 0b for binary are optional; letters can be upper or lower case. A minus sign is kept. The bit count shows how many binary digits the number needs, ignoring the sign. If you type a digit that isn't valid for the chosen base, such as 2 in binary or G in hex, the tool lists the allowed digits.

To convert decimal to another base, divide by the base repeatedly and write down the remainders from last to first. 156 in binary: 156 ÷ 2 = 78 r 0, 78 ÷ 2 = 39 r 0, 39 ÷ 2 = 19 r 1, 19 ÷ 2 = 9 r 1, 9 ÷ 2 = 4 r 1, 4 ÷ 2 = 2 r 0, 2 ÷ 2 = 1 r 0, 1 ÷ 2 = 0 r 1. Reading upward gives 10011100. Hex to binary is even easier: replace each hex digit with its four-bit pattern (9 = 1001, C = 1100, so 9C = 10011100). To see text as binary, try the binary translator.