# Binary Numbers

A binary number is a base 2 number system. This means that it only uses two symbols typically a ‘0’ and ‘1’. You may be used to the base 10 number system, most people know this as the hindu-Arabic numeral system. The base 10 number system has ten symbols 0,1,2,3,4,5,6,7,8, and 9. As such the base two number system has 2 symbols 0 and 1.

Binary codes in telecommunications and computing are used for various methods of encoding data, such as character strings into bit strings. For example the lower case character ‘b’, if represented by the bit string is 1100010.

Let’s change a number like 8 base 10 to binary.

8/ 2 = 4 Remainder 0

4 / 2 = 2 Remainder 0

2 / 2 = 1 Remainder 0

1 / 2 = 0 Remainder 1

So 8 to binary is 1000.

Let’s now take a number in binary and change it to a number in base 10. We will change **11010** base 2 or binary to base 10.

Take the binary number and reverse it (this isn’t really necessary, but makes it easy) to get **01011**

Next we are going to take those numbers and multiply them by 2 to the power of their position.

0*2⁰ +1*2¹ +0* 2²+1* 2³+1* 2⁴= 0 + 2 + 0 + 8 + 16

= 26

Looks like the binary number **11010 **is the number 26 in base 10 !

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