Binary to Decimal Converter
It is a very simple way to use this conversion tool. All you need to do is provide binary number like 110101 into the left textbox and then click on Convert button to obtain decimal value in the right textbox.
Incorrect Binary Value
You might need: Binary to Hex conversion
Binary Number System
Machines use binary number system to perform computations. This number has a base of 2. Hence, there are 2 digits in this system - 0 and 1. Each digit in binary number system represents a power of the base (2).
Decimal Number System
The base of the decimal number system is 10. In this number system, 10 digits are used - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We know that in decimal number system successive positions to the left of the decimal point represents units, tens, hundreds, etc. It is used in our day to day life.
How to convert Binary to Decimal
Let's understand the conversion by following these steps-
- Start with the rightmost digit and move towards the left by writing down 2n below it where n = 0,1,2... and so on till the left most digit.
- After this, multiply those 2n with their corresponding binary digit.
- Add all the result obtained in step 2 to get a decimal number.
The steps mentioned above will become clearer when we apply them in an example. Suppose we have a binary number 1101011 that we want to convert into decimal number.
Step i) Write down the power of 2 from right to left starting with 20.
Step ii) Multiply these 2n with their crossesponding binary digit.
Step iii) Add all the products obtained in step ii) to get the desired decimal number.
1x26 + 1x25 + 0x24 + 1x23 + 0x22 + 1x21 + 1x20 = 107
Binary to Decimal Conversion Table
The following table provides a list of few binary numbers and their corresponding decimal numbers-
| Binary Numbers | Decimal Numbers |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
