Binary Converter — Binary, Decimal, Hex & Octal

How to use the binary converter

A binary converter changes a number from one number system to another: binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8). Type a number into any box — binary, decimal, hexadecimal, or octal — and the other three update instantly. Prefixes like 0b, 0x, and 0o, spaces, and underscores are all fine. Numbers of any size stay exact, from a single bit to 64-bit values and beyond. Below the boxes you’ll find the two’s complement form for 8, 16, 32, and 64 bits and the full working for each conversion.

Binary to decimal

To convert binary to decimal, write the place values over the bits — 1, 2, 4, 8, 16 … from right to left — and add the place values wherever there’s a 1. Example: 101101 = 32 + 8 + 4 + 1 = 45. The converter shows this sum for every number you type.

Decimal to binary

To convert decimal to binary, divide by 2 again and again and write down the remainders: 45 ÷ 2 = 22 r 1, 22 ÷ 2 = 11 r 0, 11 ÷ 2 = 5 r 1, 5 ÷ 2 = 2 r 1, 2 ÷ 2 = 1 r 0, 1 ÷ 2 = 0 r 1. Reading the remainders from the bottom up gives 101101. The division table appears under the converter.

Binary to hex and hex to binary

Hexadecimal (base 16) is a shorthand for binary: every hex digit is exactly four bits. To convert binary to hex, split the bits into groups of four from the right and replace each group: 1010 1111 = AF. To go from hex to binary, expand each digit into four bits: 3C = 0011 1100. Tick Group binary in 4s to see the groups.

Binary to octal

Octal (base 8) works the same way with groups of three bits: 110 101 = 65 in octal. It’s still used for Unix file permissions (for example 755).

How to count in binary

The numbers 0 to 16 in binary, octal, and hexadecimal:

Larger numbers that come up often — 255 is the biggest value that fits in one byte:

Negative numbers: two’s complement

Computers store negative numbers using two’s complement. To find −5 in 8 bits: write 5 in binary (00000101), flip every bit (11111010), then add 1 (11111011). The first bit tells you the sign: 1 means negative. An 8-bit signed number holds −128 to 127; 16 bits hold −32,768 to 32,767. Type a negative decimal number and choose a bit width to see it.

Bits and bytes

A bit is one binary digit; a byte is 8 bits and holds 0–255. The converter shows how many bits and bytes your number needs — 255 fits in one byte, 256 needs two.

The binary clock

The live binary clock under the converter shows the current hours, minutes, and seconds in binary — a fun way to practice reading binary numbers every day.

More binary tools

Translate words and sentences with the Binary Translator, do sums with the Binary Calculator, and test yourself with the Binary Game. Everything runs in your browser — nothing is uploaded.