Binary to Decimal Calculator
Enter a binary number and instantly convert it to decimal. Supports integers and fractional values like 1011.01.
What Is a Binary to Decimal Conversion?
A binary to decimal conversion translates a number from base-2 (binary) into base-10 (decimal), the standard number system most people use every day. In binary, each digit is either 0 or 1. In decimal, digits range from 0 to 9.
Computers naturally operate in binary because electrical states are easy to represent as on/off. But humans typically read and reason in decimal. That is why this conversion is so important in programming, networking, electronics, and digital logic.
How This Binary Calculator to Decimal Works
The calculator reads your input and evaluates each bit according to its place value. In binary, place values are powers of 2:
- Rightmost integer bit is
2^0 - Next bit left is
2^1 - Then
2^2,2^3, and so on
For fractional binary numbers (values to the right of the decimal point), powers are negative:
- First bit right of the point is
2^-1 - Then
2^-2,2^-3, etc.
Manual Example: Convert 101101 to Decimal
Step 1: Assign powers of 2
For 101101, the positions from left to right are:
2^5, 2^4, 2^3, 2^2, 2^1, 2^0.
Step 2: Multiply bits by place values
1×2^5 + 0×2^4 + 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0
Step 3: Add the results
32 + 0 + 8 + 4 + 0 + 1 = 45
So, 101101₂ = 45₁₀.
Fraction Example: Convert 110.101
Integer side
110₂ = 1×2^2 + 1×2^1 + 0×2^0 = 4 + 2 + 0 = 6
Fraction side
.101₂ = 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.5 + 0 + 0.125 = 0.625
Total
6 + 0.625 = 6.625
So, 110.101₂ = 6.625₁₀.
Common Input Mistakes (and Fixes)
- Using digits other than 0 or 1: Binary cannot contain 2-9.
- Multiple decimal points: A valid number can only have one point.
- Empty input: Enter at least one binary digit.
- Extra spaces: The calculator trims leading/trailing spaces, but internal invalid characters are rejected.
When You Might Need Binary to Decimal Conversion
- Learning computer science fundamentals
- Understanding bit flags and permissions
- Working with subnet masks and IP addressing
- Debugging embedded systems and hardware data
- Preparing for coding interviews and exams
Quick Reference Table
1₂ = 1₁₀10₂ = 2₁₀11₂ = 3₁₀100₂ = 4₁₀1000₂ = 8₁₀1111₂ = 15₁₀10000₂ = 16₁₀
Final Thoughts
A binary calculator to decimal is a simple but powerful tool for anyone working with digital systems. Use the calculator above for fast conversions, and use the step-by-step breakdown to strengthen your number-system intuition.