The 10th Digital Learning Maths for IT sessions - The theme this time being the OCTAL number system which is used widely in computing circles - IP addressing being one. Some straight forward conversion tasks for you!

1. Mathematics for IT
Octal
Number
System
Unit 26
Lee Chadwick

2. Octal Number System
• Topic Definitions
• Learning Resources
• Lesson learning outcomes
• Hex Character Range
• Binary – Hex Conversion
• Hex – Binary Conversion
• Hex – Denary Conversion

3. • 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:

5. •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

6. 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

7. 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)

8. 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

9. 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.

10. 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 0
1 1 1 1
10 2 2 2
11 3 3 3
100 4 4 4
101 5 5 5
110 6 6 6
111 7 7 7
1000 10 8 8
1001 11 9 9
1010 12 10 A
1011 13 11 B
1100 14 12 C
1101 15 13 D
1110 16 14 E
1111 17 15 F

11. Why?
• Don’t forget, In octal format, each digit
represents three binary digits…
3 4 5 6
011 100 101 110

12. Octal in action:

13. Octal versus Hex:

14. 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

15. 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