How binary counts
Binary has only two digits. The places are worth 1, 2, 4, 8, 16 and so on, doubling each time.
The binary number 1011 means 8 + 0 + 2 + 1, which is 11 in decimal.
Worked example
1011 in binary is 11 in decimal, 13 in octal and B in hexadecimal.
1101 is 13, and 100000 is 32, because the sixth place from the right is worth 32.
Why hexadecimal is used
Four binary digits make exactly one hexadecimal digit, so a byte is two hex digits. 11111111 is FF, which is 255.
Octal groups three binary digits at a time. It was common on older computers and still appears in file permissions.
Inputs for the binary calculator
Binary digits
Only 0 and 1 are used. Leading zeros are allowed and do not change the value.
CALCULATOR QUESTIONS
Binary calculator questions
What is 1011 in decimal?
11. The places are worth 8, 4, 2 and 1, and 8 + 2 + 1 = 11.
How do I convert decimal to binary?
Divide by two repeatedly and read the remainders from the bottom up, or use this page in reverse by typing the decimal value on the hex page.
How many binary digits can I enter?
Up to 16. Longer strings go beyond the largest whole number a browser holds exactly.
Why is 11111111 equal to 255?
Eight ones add 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1, which is 255.