Binary to Decimal Conversion
This converter helps you convert binary numbers into decimal values and vice versa.
How to Use This Converter
- Enter a binary number (base-2) to see its decimal equivalent
- Or input a decimal number to convert it into binary
Works for both binary to decimal and decimal to binary conversions.
Understanding the Conversion
Binary numbers use base-2, where each digit is a power of 2. Like decimal numbers, the most significant digits are the leftmost ones. To derive the positional values, follow these steps:
- Find the bit position relative to the least significant bit (the rightmost digit)
- The positional value is 2 raised to the bit position
For example, these are the digit values for 8 bits (1 byte)
| Bit Position | Value |
|---|---|
| 7 | 128 |
| 6 | 64 |
| 5 | 32 |
| 4 | 16 |
| 3 | 8 |
| 2 | 4 |
| 1 | 2 |
| 0 | 1 |
Example
Convert the binary number 10110011 to decimal.
| Bit Position | Value | Binary Digit |
|---|---|---|
| 7 | 128 | 1 |
| 6 | 64 | 0 |
| 5 | 32 | 1 |
| 4 | 16 | 1 |
| 3 | 8 | 0 |
| 2 | 4 | 0 |
| 1 | 2 | 1 |
| 0 | 1 | 1 |
Adding up the positional values of the binary digits that are 1, we find that the decimal equivalent of 10110011 is 179.
Why It Matters
Binary is used internally by computers, while decimal is what humans use daily. Understanding this conversion is key for anyone learning about computing, programming, or digital electronics.