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How to Convert Binary to Decimal
Binary numbers look intimidating until you understand the pattern. Each bit is just a power of 2 that is either on (1) or off (0). Once you see that, the conversion is just addition.
The positional method
Every bit in a binary number has a positional value — a power of 2 based on where it sits. The rightmost bit is position 0 (value = 1). The next is position 1 (value = 2), then position 2 (value = 4), and so on. To convert:
- Write out the binary number.
- Label each bit with its positional value (right to left: 1, 2, 4, 8, 16…).
- For every bit that is 1, note its positional value.
- Add those values together. That is the decimal number.
Worked example: 11010110
| Bit | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| Value | 128 | 64 | 0 | 16 | 0 | 4 | 2 | 0 |
Active bits: 128 + 64 + 16 + 4 + 2 = 214
A second example: 1101
8 + 4 + 1 = 13
Common binary–decimal values
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Binary to Decimal Converter →Frequently asked questions
What is the easiest way to convert binary to decimal?
The easiest method is positional notation. Write out the binary number, then assign each bit a positional value starting from 1 on the right and doubling as you move left (1, 2, 4, 8, 16, 32, 64, 128…). Multiply each bit by its positional value and sum only the results where the bit is 1. That total is the decimal number.
How do you convert 1010 binary to decimal?
Write out the bits with their positional values: 1×8, 0×4, 1×2, 0×1. The bits that are 1 contribute: 8 + 2 = 10. So binary 1010 equals decimal 10.
How do you convert 11111111 binary to decimal?
11111111 is 8 bits all set to 1. The positional values are 128, 64, 32, 16, 8, 4, 2, 1. Sum all of them: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the maximum value of a single byte, which is why 255 appears so often in computing (e.g. RGB color values go from 0 to 255).
Why does binary use powers of 2?
Binary is base-2 — each digit position represents a power of 2 in the same way decimal positions represent powers of 10. In decimal, the columns are 1, 10, 100, 1000 (powers of 10). In binary, the columns are 1, 2, 4, 8, 16 (powers of 2). This structure lets any integer be uniquely represented as a sum of distinct powers of 2.
What is the decimal equivalent of 1 byte (8 bits)?
One byte holds 8 bits. The smallest 8-bit value is 00000000 = 0. The largest is 11111111 = 255. So a single byte can represent 256 different values (0 through 255). This is why byte-based systems like RGB colors and ASCII character codes all cap out at 255 or 256.
Can binary numbers have a decimal point (binary fractions)?
Yes — binary fractions work like decimal fractions but use negative powers of 2. The bit after the binary point represents 2^-1 (0.5), the next is 2^-2 (0.25), then 0.125, and so on. For example, 10.11 in binary is 2 + 0.5 + 0.25 = 2.75 in decimal. This guide covers whole-number conversion; fractional binary is a separate topic.