Binary to Decimal Converter
Enter a binary number to get its decimal value, with the power-of-2 working and the hex and octal forms.
Free, no sign-upRuns in your browserHow we calculate
- Binary
- 1101
- Octal
- 15
- Decimal
- 13
- Hexadecimal
- D
- Bits needed
- 4
How this was calculated
- Write the binary digits and give each one a place value of 2ⁿ, counting from 0 on the right.
- 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 1 × 2^0
- 8 + 4 + 0 + 1
- Total: 13
How to convert binary to decimal
Binary (base 2) has only two digits, 0 and 1. Each position is worth a power of 2, starting with 2⁰ = 1 on the right: 1, 2, 4, 8, 16, 32, 64, 128 and so on. To convert binary to decimal, add up the place values wherever there is a 1. This binary to decimal converter shows each place and the total as you type.
Worked example
Convert 1101. From the right the place values are 1, 2, 4 and 8, and the digits read 1, 0, 1, 1 from the right. So 1101 = 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 8 + 4 + 1 = 13. A full byte, 11111111, is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255, and 10000000 on its own is 128.
Useful reference values
- 1010 = 10 and 1111 = 15, the range of one hex digit.
- 101010 = 42, 1100100 = 100, 10000000 = 128.
- Each extra bit doubles the range: 8 bits hold 0–255, 16 bits hold 0–65,535.
Common mistakes
The most frequent error is reading the digits left to right with increasing powers; the rightmost bit is always 2⁰. Leading zeros change nothing, so 00001101 is still 13. Spaces and the 0b prefix are ignored by this tool, so you can paste values such as 0b1111 0000 (240) directly. Any digit other than 0 or 1 is flagged as an error.
Other directions
To go back, use the decimal to binary converter, which divides by 2 repeatedly and reads the remainders from last to first. For compact notation switch the target to hexadecimal, or use the hex to decimal converter. Binary values are exact up to 200 digits; negatives are shown with a minus sign rather than as two's complement.
Frequently asked questions
How do you convert binary to decimal?
Add the powers of 2 for every position that holds a 1, counting from 2⁰ on the right. For 1101 that is 8 + 4 + 1 = 13.
What is 11111111 in decimal?
255. Eight ones add 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255, the maximum value of one byte.
What is 1010 in decimal?
10. The ones are in the 8s and 2s places: 8 + 2 = 10.
Do leading zeros change a binary number?
No. 00001101 and 1101 are both 13.
How many values can n bits represent?
2ⁿ values, from 0 to 2ⁿ − 1. Eight bits give 256 values (0–255), sixteen bits give 65,536 (0–65,535).