Binary to Decimal Converter
Type a binary number to get its decimal value, with each bit’s place value added up for you.
- Binary · Octal · Decimal · Hex
- Step-by-step working
- Two’s complement
- Big numbers
What is a binary to decimal converter?
Binary to decimal conversion adds up the place values of the 1 bits. Reading from the right, the places are worth 1, 2, 4, 8, 16, 32 and so on, doubling each time. 1011 is 8 + 0 + 2 + 1 = 11. This converter does it for binary numbers of any length, shows the working with your number, and can read a bit pattern as a signed two’s complement integer of 8, 16, 32 or 64 bits.
How to convert binary to decimal
- Type a binary number in the Binary box. Prefixes, spaces and underscores are ignored.
- Read the decimal result instantly. Binary, octal, decimal, hex and a custom base update together.
- Scroll to “How to convert binary to decimal” for the step-by-step working with your number.
- For negative numbers, tick Signed and choose a bit width to see the two’s complement form. Then copy any result.
Number base cheat sheet
- Binary (base 2) uses 0–1, octal (base 8) uses 0–7, decimal (base 10) uses 0–9 and hexadecimal (base 16) uses 0–9 then A–F for 10–15.
- One hex digit is exactly 4 bits (a nibble), so hex and binary convert digit by digit: F = 1111, A = 1010.
- Common prefixes: 0b for binary, 0o for octal and 0x for hex. They are optional here.
- In two’s complement, the top bit is the sign: 1111 1111 is −1 as a signed 8-bit number but 255 unsigned.
Why use this binary to decimal converter
- Converts as you typeNo Convert button: edit either side and the other updates immediately.
- Shows the workingStep-by-step place values or repeated division for the conversion you choose, ideal for homework and exams.
- Any size, signed or unsignedArbitrary-precision integers, plus two’s complement for 8, 16, 32 and 64-bit values.
- Private by designEverything is calculated in your browser. Nothing you type is sent to a server or saved.
Common uses
- Computer science homework. Check conversions and learn place values.
- Subnet masks. Turn 11111111 11111111 11111111 00000000 into 255.255.255.0 one byte at a time.
- Permissions and flags. Read bit flags as numbers.
- Digital electronics. Convert switch and register states.
Related converters: number base converter, hex to decimal, decimal to hex, decimal to binary, hex to binary, binary to hex, binary calculator, hex calculator. Browse all encoding tools.
Example: binary to decimal
101101 (binary) = 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32 + 0 + 8 + 4 + 0 + 1 = 45 (decimal)
What to expect from the result
Whole numbers only: fractional values such as 0.1 are not converted. Very long numbers are converted exactly, but the step-by-step working is shown only for numbers up to 24 digits.
Binary to Decimal Converter questions
How do you convert binary to decimal?
Multiply each bit by its place value (1, 2, 4, 8… from the right) and add them. 1101 = 8 + 4 + 0 + 1 = 13.
What is 11111111 in decimal?
255 unsigned. As a signed 8-bit two’s complement value it is −1.
What is 1010 in decimal?
10: 8 + 0 + 2 + 0.
How do I read a negative binary number?
Tick Signed and choose the bit width. If the leftmost bit is 1, the number is negative in two’s complement.
Is there a limit on binary length?
No. Numbers are converted exactly at any length; the working is shown for up to 24 bits.