Binary to Decimal Converter

Binary is base 2 — every digit is either 0 or 1, and each position represents a power of 2 instead of a power of 10 the way decimal does. It's the native language of digital electronics: a transistor is either off (0) or on (1), so every number, character and instruction a computer handles is ultimately binary underneath.

To read a binary number as decimal, multiply each digit by the power of 2 for its position (starting from 2⁰ on the right) and add the results together.

Worked example

1010 in binary: reading right to left, positions are 2⁰=1, 2¹=2, 2²=4, 2³=8. The digits are 0,1,0,1, so the value is (1×8) + (0×4) + (1×2) + (0×1) = 10.

11111111 (eight 1s) = 128+64+32+16+8+4+2+1 = 255 — the maximum value a single byte can hold, which is why 255 shows up constantly in computing (max RGB channel value, max value of an unsigned 8-bit integer, and so on).

Where this comes up

• Computer science coursework and interview prep — binary arithmetic is a standard fundamentals topic
• Reading raw binary data dumps, network packet captures or microcontroller register values
• Understanding IP subnet masks, permission flags and bitwise operations, which are all expressed in binary