Mathematics for IT

OctalNumberSystem

Unit 26

Lee Chadwick

Octal Number System

• Topic Definitions• Learning Resources• Lesson learning outcomes• Hex Character Range• Binary – Hex Conversion• Hex – Binary Conversion• Hex – Denary Conversion

• Hexadecimal: "Hexadecimal" means "based on 16" (From Greek hexa: "six" and Latin decima: "a tenth part").

• Decimal: Based on 10; Example: the numbers we use in everyday life are decimal numbers, because there are 10 of them (0,1,2,3,4,5,6,7,8 and 9).

• Denary:Same as Decimal – Base 10 • Binary: The word binary comes from "Bi-" meaning two. We see "bi-" in

words such as "bicycle" (two wheels) or "binocular" (two eyes). Binary only uses 2 digits; 1 & 0

• Octal: An Octal Number uses only these 8 digits: 0, 1, 2, 3, 4, 5, 6 and 7 Examples:

• 10 in Octal equals 8 in the Decimal Number System.• 167 in Octal equals 119 in the Decimal Number System. Also called Base 8.

Definitions:

Octal

Data Representation

Learning Aims:• Identify the concept of Octal• Establish the purpose of Octal• Compare Base 2, Base 10, Base 8 and Base 16• Convert Octal to Binary and Denary – And Back

By the end of this session you will: Be able to convert positive denary whole numbers (0-255) into Octal numbers and vice versa Be able to convert between binary and Octal equivalents of the same number

Be able to explain the use of Octal numbers to represent binary numbers

Number Bases• Binary: Base 2

(0, 1)

• Octal: Base 8

(0, 1, 2, 3, 4, 5, 6, 7)

• Decimal: Base 10

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

• Hexadecimal: Base 16

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)

What is Octal?• Refers to the base-8 numbering system, which

uses just eight unique symbols:

• Programs often display data in Base-8 formats because it is relatively easy for humans to read and can easily be translated into binary format, which is the most important format for computers.

0 1 2 3 4 5 6 7

Convert Octal to Binary• By contrast, decimal format is the easiest

format for humans to read because it is the one we use in everyday life.

• Translating between decimal and binary formats is relatively difficult.

• In octal format, each digit represents three binary digits.

Convert Octal to Binary

• With this table it is easy to translate between octal and binary. For example, the octal number 3456 is: 011 100 101 110 in binary.

Binary Octal Decimal Hexadecimal(Base 2) (Base 8) (Base 10) (Base 16)

0 0 0 01 1 1 110 2 2 211 3 3 3100 4 4 4101 5 5 5110 6 6 6111 7 7 71000 10 8 81001 11 9 91010 12 10 A1011 13 11 B1100 14 12 C1101 15 13 D1110 16 14 E1111 17 15 F

Why?• Don’t forget, In octal format, each digit

represents three binary digits…

3 4 5 6

011 100 101 110

Octal in action:

Octal versus Hex:

Task:• Convert these Binary values to Octal:

• 111 111 111 111• 001 001 100 100• 010 001 101 011

• Convert these Octal values to Binary:• 1234• 7963• 2746

Number Systems – Task:Number Systems Working Together

Using a structured approach, complete a range of conversions between the number systems discussed previously. The conversions needed are:• Decimal to Binary, Octal, Hexadecimal• Binary to Decimal, Octal, Hexadecimal • Octal to Decimal, Binary, Hexadecimal• Hexadecimal to Decimal, Binary, Octal