Binary to decimal

Reading a bit pattern as a number

Read a base-two whole number as an exact decimal integer. Use this direction to understand the numerical value of a binary string from a specification, flag field or programming exercise. Only zeroes and ones are digits; an optional 0b prefix marks the base. The converter accepts an optional leading minus sign but does not infer whether a fixed-width field was intended as signed.

Each binary digit contributes its bit value multiplied by a power of two. In 11111111, the set positions have weights 128, 64, 32, 16, 8, 4, 2 and 1. Adding them gives 255. A leading zero would not change that value, but it might matter to the size of a field in a protocol; this numeric converter intentionally ignores such width. If the bit groups represent UTF-8 bytes of text, use the separate binary-to-text tool instead. For a concrete check, the example input 11111111 produces 255. Keep the original beside the result when comparing it with another application.

What a number base changes

Decimal, binary and hexadecimal are different written forms of the same integer. Decimal has ten digits, binary has two, and hexadecimal has sixteen symbols, adding A through F after 0 through 9. The value itself does not change when its notation changes. A bit is a binary digit; four bits correspond to one hexadecimal digit, which makes hex compact for memory addresses, bit masks and debugging. Use these converters when a specification, log or programming language displays a number in a base other than the one you are reading.

Reading signs and widths correctly

The sign is written separately; these results are not fixed-width two’s-complement machine integers. These converters work with whole integers and retain arbitrary precision through BigInt, so a long value does not silently lose low bits as an ordinary floating-point number might. A leading minus sign represents a negative mathematical integer. It is not a fixed-width two’s-complement byte pattern: the bit string for minus one depends on whether a machine uses eight, sixteen, thirty-two or another number of bits. Add a width and encoding rule separately if a protocol requires one. Do not confuse the binary value of an integer with UTF-8 binary bytes of the characters used to spell it.