About binary to decimal converter
Binary uses only 0 and 1. To read it in decimal, add up the place values where a 1 appears. For example 1011 = 8 + 2 + 1 = 11.
Worked example
Take 11010110. The places with a 1 are 128, 64, 16, 4 and 2. Adding them: 128 + 64 + 16 + 4 + 2 = 214. A quick check: an 8-bit binary number can be at most 11111111, which is 255, so the answer must be 255 or less. Binary 10000000 is exactly 128, and each extra leading digit doubles the value.
How place values work
Each digit position is worth a power of the base. In decimal the places are 1, 10, 100, 1000 and so on. In binary they are 1, 2, 4, 8, 16, and in hexadecimal 1, 16, 256, 4096.
Why binary matters
- Computers store everything as binary; hexadecimal and octal are compact ways to write it.
- One hex digit equals exactly four binary digits, which is why programmers use it for colours, memory addresses and byte values.
- Octal groups three bits per digit and appears in Unix file permissions such as 755.
