Binary ↔ Decimal ↔ Hex ↔ Octal Converter

Multiply each binary digit by 2 raised to its position power, then sum the results. For example, 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10. This tool shows every step of the calculation.

They are different number bases: binary (base 2) uses only 0 and 1, octal (base 8) uses 0–7, decimal (base 10) uses 0–9 (our everyday system), and hexadecimal (base 16) uses 0–9 and A–F. Computers work natively in binary; hex is a compact shorthand for binary (4 bits = 1 hex digit).

Repeatedly divide the number by 2 and record each remainder. Read the remainders from bottom to top. For example: 172 ÷ 2 = 86 r0, 86 ÷ 2 = 43 r0, 43 ÷ 2 = 21 r1, 21 ÷ 2 = 10 r1, 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1 → read up: 10101100.

Binary strings get very long quickly — a 32-bit number needs 32 digits in binary but only 8 in hex. Each hex digit represents exactly 4 binary bits (a nibble), making conversion simple and the representation compact. Memory addresses, color codes (#FF6600), and byte values are all expressed in hex.

A nibble is 4 binary bits (one hex digit), representing values 0–15. A byte is 8 binary bits (two hex digits), representing values 0–255. A byte is the fundamental unit of digital data storage.