Binary to decimal converter

Type a binary number to see its decimal value — or a decimal number to see its binary form — with the powers-of-two expansion worked out below. 0b prefixes, spaces and underscores are accepted.

How binary to decimal conversion works

Binary is base 2: each position is worth a power of two, doubling from right to left — 1, 2, 4, 8, 16, and so on. Add up the values of the positions holding a 1:

101011₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 32 + 8 + 2 + 1 = 43₁₀

Decimal to binary works by dividing by 2 repeatedly and reading the remainders from bottom to top — the converter shows those division steps for your number.

First powers of two

Binary values worth recognizing

Round powers of two and "all ones" patterns are the ones that show up in limits and masks:

See the full 0x00–0xFF table

Related tools and guides

• Hex ↔ decimal converter — the same number, four bits per hex digit.
• Hex ↔ binary converter — group those bits into nibbles.
• Integer ranges and powers of two — 2⁰ to 2⁶⁴ and the int8–uint64 limits.
• Two's complement calculator — negative numbers in binary.
• Bitwise operations explained — what AND, OR and XOR do with each bit.