11 octal number system

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:

4. Octal Data Representation

5. 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

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. 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) 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