Convert Binary to Decimal
Convert binary to decimal quickly and easily. Enter a base 2 number using just 0 and 1. This binary to dec calculator will find the base 10 decimal value for you.
Binary to decimal converter
Quick Reference
Binary to Decimal Conversion Table
Here are some common binary numbers converted to decimal. This chart saves you time on simple math.
| Binary | Calculation | Decimal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 10 | 1×2¹ + 0×2⁰ | 2 |
| 11 | 1×2¹ + 1×2⁰ | 3 |
| 100 | 1×2² | 4 |
| 101 | 1×2² + 1×2⁰ | 5 |
| 110 | 1×2² + 1×2¹ | 6 |
| 111 | 1×2² + 1×2¹ + 1×2⁰ | 7 |
| 1000 | 1×2³ | 8 |
| 1010 | 1×2³ + 1×2¹ | 10 |
| 1111 | 1×2³ + 1×2² + 1×2¹ + 1×2⁰ | 15 |
| 10000 | 1×2⁴ | 16 |
| 11001 | 1×2⁴ + 1×2³ + 1×2⁰ | 25 |
| 111111 | 32 + 16 + 8 + 4 + 2 + 1 | 63 |
| 11111111 | 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 | 255 |
How it works
How to Convert Binary to Decimal
Want to know how to calculate binary to decimal by hand? The process works by adding up powers of 2.
The Method
Computers use binary. This is a base 2 number system built on zeros and ones. We use decimal in our daily lives. That is a base 10 system with digits zero through nine. To change a binary number to decimal, you multiply each digit by its place value and add them up.
Starting from the right side, each position represents a power of 2. These go 2⁰, 2¹, 2², 2³, and so on.
How to Turn BIN into DEC
Write the binary number
Take the binary value you want to convert. For example, let us use 1010.
Assign powers of 2
Look at your number from right to left. The place values are 1, 2, 4, and 8.
Add the active values
Multiply the digits by their place values. For 1010 you add 8 and 2. This means 1010 in binary equals 10 in decimal.
Binary vs Decimal
What Is the Difference Between Binary and Decimal?
Binary and decimal are just two different ways to count. Binary uses base 2. It only relies on the digits 0 and 1. Decimal uses base 10. It relies on the digits 0 through 9.
Computers read binary naturally. Their hardware processes everything as off or on states.
Decimal is what we use for everyday math and money. You can translate any value between these two systems. A simple binary decimal conversion calculator does the heavy lifting for you.
Worked Examples
Sample Calculations
Let us look at a few more examples. These show how to convert a binary number into decimal form.
10 in binary to decimal
The math is simple. 1 times 2 plus 0 times 1 equals 2.
101 in binary to decimal
You add 4 and 1. The decimal value is 5.
1000 in binary to decimal
You just have one active bit in the 8 position. The answer is 8.
1010 in binary to decimal
Add 8 and 2 together. You get 10 in decimal.
1111 in binary to decimal
Add 8, 4, 2, and 1. This equals 15 in decimal.
10000 in binary to decimal
The active bit sits in the 16 position. The answer is 16.
11001 in binary to decimal
Add 16, 8, and 1. You get 25.
11111111 in binary to decimal
Add up all the place values from 128 down to 1. You get 255.
FAQ
Frequently Asked Questions
Everything you need to know about calculating binary to decimal.