Binary to Decimal Converter
Binary (base 2) is the native number system of digital computers, using only the digits 0 and 1. To read a binary number as the decimal value people use every day, each bit is weighted by a power of two according to its position. This converter takes a binary string and returns the decimal value, the hexadecimal equivalent, the octal equivalent, and the bit length. The conversion is a simple positional sum: the rightmost bit is worth 1, the next 2, the next 4, and so on, doubling at each step to the left.
Binary to decimal formula
Decimal = sum of (bit * 2 ^ position)
Position counts from 0 at the rightmost bit
Place values: 1, 2, 4, 8, 16, 32, 64, 128, ...
Example: 1011 = (1*8) + (0*4) + (1*2) + (1*1) = 11
Hexadecimal = decimal value rewritten in base 16
Each binary digit either adds its place value (when the bit is 1) or contributes nothing (when the bit is 0).
Binary number context
- Computers store and process all data as binary, the two-state on or off of transistors.
- An 8-bit byte holds 256 values (0 to 255); a 16-bit value holds 65,536.
- Binary maps cleanly to hexadecimal: four bits equal one hex digit.
- Network addresses, file permissions, and bit flags are often reasoned about in binary.
- Leading zeros do not change a binary value: 0011 and 11 are both decimal 3.
Binary to decimal converter: frequently asked questions
How do you convert binary to decimal?
Multiply each bit by 2 raised to the power of its position, counting from zero at the rightmost bit, then add the results. The binary 1011 equals 1 times 8 plus 0 times 4 plus 1 times 2 plus 1 times 1, which is 8 plus 0 plus 2 plus 1, equal to 11 in decimal.
What is the place value of each binary digit?
Reading from the right, the place values are 1, 2, 4, 8, 16, 32, and so on, each double the previous. These are the powers of two. The leftmost bit of an 8-bit number carries a place value of 128.
What is the largest 8-bit binary number?
The largest 8-bit value is 11111111, which equals 255 in decimal (2 to the power of 8 minus 1). An 8-bit number can represent 256 distinct values, from 0 to 255.
What characters are valid in a binary number?
Only the digits 0 and 1 are valid in binary. Any other character, including spaces inside the number or letters, makes the value invalid. This converter ignores surrounding whitespace but rejects non-binary digits.
How many bits are in a byte?
A byte is 8 bits. Two bytes make 16 bits, four bytes make 32 bits, and eight bytes make 64 bits. The bit length output of this converter tells you how many binary digits your value uses.
Official sources
- NIST: National Institute of Standards and Technology, positional number systems reference.
- IETF RFC Editor: RFC 4648, data encodings and base representations.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.