Appendix B

Number Systems

Introduction

Decimal System: We use the decimal system in our daily lives. The allowable digits in decimal system are:

0 1 2 3 4 5 6 7 8 9. The base is 10. The lowest number = 0 ; the highest number = 9. The counting goes 0...99, 100 and so on.

Binary System: The computer uses the binary system for its internal representation. The digits allowed are: 0 1. The base is 2. The lowest number = 0 ; the highest number = 1. The counting goes: 0 1 10 11 100 101 110 111 1000... The count is shown in Table B.1.

Table B.l Decimal numbers and their binary equivalents

Computer uses two other representations, namely Octal and Hexa decimal system for addressing mechanisms, storage and display the results to users if required.

Octal System: Base is 8. This is equivalent to 2³. Therefore, 3 digits are required for octal representation. The lowest number = 0; the highest number = 7. The counting is shown below in Table B.2.

Table B.2 Octal numbers and their binary equivalents

Hexa decimal System: Base is 16. This is equivalent to 2⁴. Therefore, 4 digits are required for Hexa-decimal representation. The lowest number = 0; the highest number = 15. The counting is shown below in Table B.3.

Table B.3 Hexa-decimal numbers and their binary equivalents Appendix C