Basic Prog. Sys. © copyright M.J.Morris 2017
Two State Devices and Binary Numbers. It was not technologically feasible to design systems that could represent numbers using the decimal system which is most familiar to us. (This would have required components that could be set to ten different states, to represent digits 0-9). The components that digital electronics systems are based on only have two different states that they can be set to, (e.g. a switch can either be on or off etc.). A two state device can only represent two different digits. Therefore the number system that we use with digital electronics, is the binary numbering system, which only has two digits (0 & 1). Not all of the components used in digital systems are inherently limited to two states. For example the magnetic strength of the elements on hard disk drives, can theoretically have an infinite number of different values between their minimum and maximum levels. However in digital systems, we treat them as two state devices, by only distinguishing between whether an element has a north or south magnetic pole. Further examples of components used as two sate devices in digital systems. Capacitor - charge/uncharged. Light - source on/off. Reflective surface - reflective /non reflective.
Binary numbers. A detailed understanding of binary numbers is required for an in depth study of computer systems and this is covered in the “maths for computer science” module. However, the introduction given below is sufficient for the material covered in the remainder of this section. (If you are unfamiliar with numbers raised to powers, then please refer to the basic “maths for science” module).
The decimal numbering system. The digits in a decimal number have 10 possible values (0-9). Each digit in a number represents a multiple of a power of 10. i.e. The right hand digit is x 100 , then as we move left the power of 10 increases x101 , x102 etc. e.g. in the number 257: The digit 2 = 2 x102 = 2 x 100 = 200. The digit 5 = 5 x101 = 5 x 10 = 50. The digit 7 = 7 x100 = 7 x 1 = 7.
The binary numbering system. The digits in binary numbers have only two possible values (0 & 1) and the different digit positions represent different powers of 2. e.g. x 20 , x 21 , x 22 etc. So the value of each of the digits in the number 101 binary (when written in decimal) would be: 1 x 22 = 1 x 4 = 4. 0 x 21 = 0 x 2 = 0. 1 x 20 = 1 x 1 = 1. The overall decimal value would be 4 + 0 + 1 = 5. i.e. 101 binary = 5 decimal. A single binary digit is called a bit and an 8 bit binary number is called a byte