Binary to Decimal Converter
Convert binary numbers (base 2) to decimal numbers (base 10) instantly using our easy tool.
Understanding the Binary to Decimal Transformation
Have you ever wondered how computers translate a series of ones and zeros into numbers we actually recognize? This process is known as Binary to Decimal conversion. While machines live in a world of “on” and “off” (Base-2), humans operate in Base-10.
In this guide, we will break down the logic behind the math so you can perform these conversions manually or understand how a digital converter works.
The Core Logic: Positional Notation
Both systems are “positional,” meaning a digit’s value depends on where it sits.
- In Decimal, the positions represent the 1s, 10s, 100s, and so on.
- In Binary, the positions represent the Powers of 2.
The Binary Weight Scale
To convert any binary string, you simply need to remember the doubling sequence starting from the right:
… 128, 64, 32, 16, 8, 4, 2, 1
The Step-by-Step Conversion Process
To turn binary into decimal, follow this “Multiply and Add” method:
- List the Powers of 2: Write down the powers of 2 from right to left, starting with 1 ($2^0$), then 2 ($2^1$), 4 ($2^2$), etc.
- Align the Binary: Place your binary digits directly under these numbers.
- Filter the Values: Ignore any power of 2 that has a 0 under it.
- Sum the Remainder: Add up all the power-of-2 values that have a 1 under them.
Example: Converting 11010
Let’s see it in action with the binary number 11010:
| Power of 2 | 16 | 8 | 4 | 2 | 1 |
| Binary Digit | 1 | 1 | 0 | 1 | 0 |
| Value to Add | 16 | 8 | 0 | 2 | 0 |
The Math: $16 + 8 + 2 = 26$
Result: 11010 in binary is 26 in decimal.
Why is this Conversion Important?
Understanding this conversion is the “Hello World” of digital literacy. It is used in:
- IP Addressing: Converting binary strings into readable IPv4 addresses.
- Coding: Understanding how data types (like Integers) are stored in memory.
- Hardware Design: Designing circuits that translate user input into machine instructions.
Common Conversions for Quick Reference
| Binary | Decimal | Tip |
0000 | 0 | All bits off |
0111 | 7 | Sum of 4+2+1 |
1010 | 10 | Standard “Ten” |
1111 | 15 | Max 4-bit value |
10000 | 16 | The next power of 2 |