Number Base Converter

What is binary?

Binary is base 2, which uses only the digits 0 and 1. Computers store data this way because circuits have two states. The decimal number 10 is 1010 in binary, and 255 is 11111111.

What is hexadecimal used for?

Hexadecimal is base 16, with digits 0 to 9 and letters A to F for 10 to 15. Each hex digit stands for exactly four bits, so a byte is two hex digits. 255 is FF, and web colours such as #FF5733 are three hex bytes.

How do I change decimal to binary by hand?

Divide by 2 repeatedly and note the remainders, then read them bottom to top. For 13: 13 ÷ 2 = 6 r1, 6 ÷ 2 = 3 r0, 3 ÷ 2 = 1 r1, 1 ÷ 2 = 0 r1, giving 1101. The tool does this and also shows hex and octal.

What is octal used for?

Octal is base 8, with digits 0 to 7, and each digit equals three bits. It survives in Unix file permissions: decimal 493 is octal 755, i.e. 111 101 101 in binary, meaning read-write-execute for the owner and read-execute for the group and others.

How does the tool treat negative numbers and decimals?

It keeps the minus sign and drops any fractional part, truncating toward zero. -10 gives -1010 in binary, -A in hex and -12 in octal, and 3.7 is treated as 3. That is a signed representation and not two’s complement. For fixed-width forms, such as -1 in 8 bits, you need to work out the bit pattern yourself.

Can I type a hex or binary number to get decimal?

No. The input is a decimal number only, and the tool shows the other bases as results. To go from hex to decimal, multiply each digit by a power of 16 and add: FF is 15 × 16 + 15 = 255.

What is the largest number it accepts?

9,007,199,254,740,991 (2^53 − 1). Beyond that, the browser’s numbers cannot hold every whole value exactly, so the tool shows an out-of-range message instead of a wrong answer.