What is a Binary Number?
A binary number is a number that consists of only 1s and 0s. Binary numbers use the base 2 system (hence the "bi" in binary), as opposed to decimal numbers that use the base 10 system.
In other words, the decimal system (base 10) uses only the digits 0,1,2,3,4,5,6,7,8 and 9, whereas the binary system (base 2) uses only the digits 0 and 1.
To differentiate between a base 2 and a base 10 number, base 2 numbers are usually written with a 2 as the subscript. For example, 1012 would tell you that the number is the binary number one-zero-one, and not the decimal number one-hundred-one.
How to Convert Binary to Decimal
To help you to understand how to convert binary to decimal, it may help to look at how we translate the value of a decimal number. Let's use the decimal number 1234 (123410, or one-thousand, two-hundred and thirty-four) as an example:
Translating the Value of a Decimal (base 10) NumberWith the above base 10 translation in mind, here is how you would convert the base 2 number 1111 (11112 or one-one-one-one) into a base 10 number:
Converting a Binary (base 2) to a Decimal (base 10)Adding the values of line D we get the base 10 number of 15. In other words, the number 11112 coverts to the number 1510.
As you can see, converting a binary number to a decimal number is a simple process of identifying the place value of each digit, multiplying each digit by its place value, and then adding up all of the products.
Converting Base 2 Numbers That Have Decimal Points
If the base 2 you want to convert has a decimal point in it, you simply continue subtracting 1 from each exponent (line A below) as you move from left to right. For example, here is how you would convert 111.1012 into its base 10 equivalent:
Converting a Binary That Has a Decimal PointAdding the values of line D we get the decimal number 7.625. In other words, the number 111.1012 coverts to the number 7.62510. Note that the red exponents in line A indicate digits that are located to the right of the decimal point.
So you see, in a binary number each place value to the right of the decimal point decreases by 1/2 (--> 1/2, 1/4, 1/8, etc.) as opposed to the place values to the left of the decimal point whose values double with each place you move to the left (8, 4, 2, 1 <--).
