Convert between binary and decimal number systems. Also shows octal and hexadecimal equivalents.
Enter a binary number or a decimal number to convert between the two systems. Octal and hex equivalents are shown as well.
A binary to decimal converter translates numbers between the base-2 system used
by computers and the base-10 system humans use every day. Enter a binary string
like 11010110 and get 214, or enter a decimal number and see its binary
representation.
The converter also shows the octal (base-8) and hexadecimal (base-16)
equivalents, making it a complete number base conversion tool. This is
invaluable for computer science students, programmers debugging bit patterns,
and anyone studying digital logic.
Binary is the foundation of all digital computing — every file, image and
instruction ultimately reduces to sequences of 0s and 1s. Understanding binary
conversion is a core skill in computer science and electrical engineering.
How to use
Choose Binary → Decimal or Decimal → Binary.
Enter the number to convert.
Read the result plus octal and hex equivalents below.
Formula
Binary uses base 2; decimal uses base 10.
Binary to DecimalSum each bit × 2^position (right to left, starting at 0)
Decimal to BinaryRepeatedly divide by 2, read remainders bottom-up
Worked examples
11010110 to decimal
Binary 11010110 = 128 + 64 + 16 + 4 + 2 = 214 in decimal, D6 in hex, 326 in octal.
255 to binary
Decimal 255 converts to 11111111 in binary (8 bits all set), FF in hex, 377 in octal.
Frequently asked questions
How do I convert binary to decimal?
Multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right), then sum the results. For example, 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11.
How do I convert decimal to binary?
Repeatedly divide the number by 2 and record the remainders. Read the remainders from bottom to top for the binary result.
What is the binary number system?
Binary (base-2) uses only the digits 0 and 1. It is the fundamental language of computers, where each digit (bit) represents an on/off state.
What is the largest decimal number with 8 bits?
With 8 bits, the maximum unsigned value is 11111111 in binary, which equals 255 in decimal.
What are octal and hexadecimal?
Octal is base-8 (digits 0–7) and hexadecimal is base-16 (digits 0–9, A–F). They are shortcuts for grouping binary digits — 3 bits per octal digit and 4 bits per hex digit.