1. Types of data representation- introduction

posted Jun 30, 2014, 9:42 PM by Maurice Nyamoti   [ updated Jun 30, 2014, 11:02 PM ]


Number systems and their representation

As stated earlier in the chapter, computer represent data in a form that can be manipulated either logically or mathematically. There are various forms, however here we are going to discuss 4 of them as provided by the syllabus.

Classifications of number systems

Decimal number system

Decimal number system has ten digits ranging from 0-9. because this system has ten digits. its also called base 10 number system or denary number system.

Binary number system

Binary is another way of saying Base Two. So, in a binary number system, there are only two symbols used to represent numbers: 0 and 1. When we count up from zero in binary, we run out of symbols much more frequently.

Octal number system

Octal is another number system with less symbols to use than our conventional number system. Octal is fancy for Base Eight meaning eight symbols are used to represent all the quantities. They are 0, 1, 2, 3, 4, 5, 6, and 7. When we count up one from the 7, we need a new placement to represent what we call 8 since an 8 doesn't exist in Octal.

Hexadecimal number systems

The hexadecimal system is Base Sixteen. As its base implies, this number system uses sixteen symbols to represent numbers. Unlike binary and octal, hexadecimal has six additional symbols that it uses beyond the conventional ones found in decimal. But what comes after 9? 10 is not a single digit but two… Fortunately, the convention is that once additional symbols are needed beyond the normal ten, letters are to be used. So, in hexadecimal, the total list of symbols to use is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. In a digital display, the numbers B and D are lowercase.

When counting in hexadecimal, you count 0, 1, 2, and so on. However, when you reach 9, you go directly to A. Then, you count B, C, D, E, and F. But what is next? We are out of symbols! When we run out of symbols, we create a new digit placement and move on. So after F is 10. You count further until you reach 19. After 19, the next number is 1A. This goes on forever.