Boolean values were very easy, but unfortunately, for numbers, it's quite a different story. In this lesson, we will only cover unsigned integers, and in the next lesson, we will (hopefully) cover the other types. Before we start, though, we need to learn about numeral systems.
Numeral systems are a way of representing a number. They are distinct from number systems, which are about the numbers themselves, and not how we represent the numbers. (Real and complex are the two major number systems.) Numeral systems include the denary system (a.k.a. decimal system), the binary system, the octal system and the hexadecimal system. For this lesson, we will cover only the binary system. Hopefully, we'll cover the hexadecimal system in a future lesson.
You've probably noticed that 'decimal', 'binary', 'octal' and 'hexadecimal' all contain number prefixes. What do they mean? To illustrate, let's start with the denary system, which is the system we use every day.
Each digit of a real number has a place value which determines its actual value. Place value increases exponentially to the left. For example, in 123410, 4 has a place value of 100, 3 has a place value of 101, 2 has a place value of 102 and 1 has a place value of 103. The base of the place value is also the base of the numeral system, in this case 10 (hence the little 10 after 1234).