When you think about it, it's truly arbitrary how we count. The number system we are used to using is called decimal (dec = 10) and therefore we get to use ten numbers from 0 to 9. That's why it's called binary because there are only two numbers like there are only two wheels on a bicycle. Therefore a computer at it's very basic level can only count using a 0 (off) or a 1 (on). Those memory chips in computers are actually made of rows upon rows of circuits that are either on at some voltage or off at some voltage. That's the beauty of our digital age, it's either "on" or it's "off". When it comes to computers and therefore PLCs they can only store in memory a 0 or a 1. You get the point? Therefore, if you had three apples then the third apple would be designated as 10 when in reality you only have three apples to eat. How would you count anything? You'd have to do it like 0, 1, 10, 11, 100, 101, 110, 111 and so on. Pretend that the evil goblin of number snatchers had taken every number from two to nine. How? Consider if you had no choice but to count with only a zero or a one.
You see, in the binary number system 10 = 2. If you don't get this joke then hopefully by the end of the chapter you'll get a chuckle out of it.
"There are 10 types of people in the world: Those who understand binary, and those who don't." Binary People: Learning your 1's and 0's Introduction