Binary

Binary is the base-2 numbering system. That means each digit can have one of two values: 0 or 1.

To calculate the value of positional numbers, we calculate the actual values of its digits and add them together. To find the actual value of a digit, we multiply the digit ($d$) by the base ($b$) to the power of the digit's position ($p$):

$$d\times b^p$$

Example

Binary is the base-2 numbering system, so $b=2$. Given the binary number 011, we can calculate its value like so:

$$(0\times 2^2)+(1\times 2^1)+(1\times 2^0)=0+2+1=3$$

Tools

• Binary Calculator

Further reading

• Positional Notation