Each binary digit is a power of two: reading right to left, the places are worth 1, 2, 4, 8, 16 and so on. Adding the places that hold a 1 gives the decimal value. This converter does it for numbers of any length.
How to use the Binary Converter
- Number
- Input base
- Convert to
- Two’s complement width
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How it works
The number is read exactly using arbitrary-precision integers (so very long values are not rounded), then written in each base. Two’s complement shows how a negative number is stored in the chosen number of bits.
Formula
value = Σ digit × base^positionTo convert: divide repeatedly by the new base and read the remainders in reverse.Worked example
Inputs — Number: 11111101010; Input base: Binary (2); Convert to: Decimal (10); Two’s complement width: No fixed width.
Results — Result = 2026; Binary = 111 1110 1010; Octal = 3752; Decimal = 2,026; Hexadecimal = 7EA; Bits needed = 11.
Key terms
- Bit
- A binary digit, 0 or 1.
- Nibble
- Four bits, one hexadecimal digit.
- Two’s complement
- The standard way computers store negative integers.
Frequently asked questions
What is 255 in binary?
1111 1111.
What is FF in decimal?
255.
How do I convert binary to hex by hand?
Split the bits into groups of four from the right and replace each group with its hex digit (0000 = 0 … 1111 = F).
What formula does the Binary Converter use?
value = Σ digit × base^position.