Binary to Decimal
Converts a binary number to decimal.
Formula
Variables
Example
1011₂ = 11
How it works
A binary number is built from powers of 2, not powers of 10. In the formula, each bit is multiplied by its place value, starting with 2^0 on the right, so a 1 means that power of 2 is included and a 0 means it is skipped. Adding all the included powers gives the equivalent decimal value.
When to use it
Use this when translating a binary number from computers into the decimal system people commonly use. It is also useful when checking binary answers in programming, digital electronics, or computer architecture.
Worked example, step by step
Convert 11010₂ to decimal = (1 × 2^4) + (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (0 × 2^0) = 16 + 8 + 0 + 2 + 0 = 26 So, 11010₂ = 26₁₀
Common mistakes to avoid
- Starting the rightmost bit at 2^1 instead of 2^0
- Treating binary digits like decimal digits and adding them directly
- Forgetting to include positions with 0, which can lead to miscounting place values
Did You Know?
Computers use binary because transistors have two stable states — on and off, 1 and 0.
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