VJC Chapter 9 Data Representation

VJC/H2Computing/9569 Chapter 9: Data Representation Contents 1 Number systems 1.1 Denary numbers 1.2 Binary numbers 1.3 Hexadecimal numbers 2 Conversion 2.1 Denary to Binary 2.2 Binary to Denary 2.3 Hexadecimal to Binary 2.4 Binary to Hexadecimal 2.5 Denary to Hexadecimal 2.6 Hexadecimal to Denary Syllabus Learning Outcomes 3.1 Data Representation Understand that values can be represented in different number bases: denary, binary and hexadecimal. 3.1.1 Represent data in binary and hexadecimal forms. 3.1.2 Write programs to perform the conversion of positive integers between different number bases: denary, binary and hexadecimal forms; and display results. 1

VJC/H2Computing/9569 1 Number systems In this chapter, we will learn about three number systems – denary, binary and hexadecimal. Learning about number systems will allow you to understand how computers represent data and how to interpret them. 1.1 Denary numbers The number system that we are most familiar with and typically used is called the denary number system. It is also known as the decimal number system and is made up of 10 distinct digits – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This is therefore a base 10 number system. Consider a denary number 346. The table below shows the representation of the denary number using place values. Place value 10 2 = 100 10 1 = 10 10 0 = 1 Digit 3 4 6 Product of digit and place value This gives 1.2 Binary numbers The number system used by computers consists of two unique digits – 0 and 1. It is called the binary number system. A binary digit is referred to as a bit. A group of eight bits is called a byte. Humans tend to use the denary number system. Hence, denary numbers must be converted into their binary equivalent before a computer can use them. As with a denary number, the value of a binary number is defined by place values. Consider the binary number 101110. Place value 2 5 = 32 2 4 = 16 2 3 = 8 2 2 = 4 2 1 = 2 2 0 = 1 Digit 1 0 1 1 1 0 Product of digit and place value This gives 2

VJC/H2Computing/9569 1.3 Hexadecimal numbers There is another number system, called the hexadecimal number system. This number system consists of 16 unique digits – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The symbols A through to F represent the denary values 10 to 15. Hexadecimal digit 0 1 2 3 4 5 6 7 8 9 A B C D E F Denary eq