Binary, Decimal, Hex & Octal Converter

About the Binary, Decimal, Hex & Octal Converter

Computers store and process data using Binary (Base-2) digits (0 and 1), while programmers and engineers frequently represent binary bytes compactly using Hexadecimal (Base-16) (digits 0–9 and A–F) and Octal (Base-8).

Our Base Converter translates any integer between Decimal, Binary, Hexadecimal, and Octal and displays the exact bit length.

Positional Number Base Formulas

In any base b, a sequence of digits d_k ... d_1 d_0 represents a sum of powers of b:

How to Convert Between Decimal, Binary, and Hexadecimal

1. Decimal to Binary: Divide the decimal number by 2 repeatedly, recording the remainder (0 or 1) at each step until the quotient is 0. Read the remainders in reverse order.
2. Binary to Decimal: Multiply each binary bit by its positional power of 2 (1, 2, 4, 8, 16, 32, 64, 128…) and add them together.
3. Binary to Hexadecimal: Group the binary bits into sets of 4 from right to left and convert each 4-bit nibble into a single hex digit (0000 = 0 through 1111 = F).

Worked Example: The decimal number 255 equals 11111111 in 8-bit binary and 0xFF in hexadecimal.

Frequently Asked Questions (FAQ)

Why do programmers use hexadecimal instead of binary?

Each hexadecimal digit corresponds to exactly 4 binary bits (one nibble), so an 8-bit byte (like 11111111) can be written concisely as just two hex digits (FF).