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Number bases - hex

What am I Learning today?

I am learning how to explain why hexadecimal is often used in computer science.
I am learning how to understand how hexadecimal can be used to represent whole numbers.
I am learning how to convert in both directions between binary and hexadecimal.

Knowledge Organiser

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Lesson

Task 1 - Getting Organised - PowerPoint Click to see more

  1. Set your Learning Objectives to red.

  2. We are going to save all of our work for this topic into this PowerPoint.

  3. To download the PowerPoint by clicking on the image below

    Access denied.
  4. Save your PowerPoint as 'Programming 1'


Task 2 - Introducing hexadecimal Click to see more

Visualizing Base-16

Although numbers are processed inside a computer as binary, that doesn’t mean that we need to always represent these numbers as binary to humans.


Task 1

  • Click on the image below to try the number base abacus
    1. Change the base in the top left corner to 16
    2. Create on the abacus and then screenshot the following base 16 numbers
    • 5 - 256, 3 - 4096, 4 - 16, 6 - Units
    • 6 - 16, 9 - 256 6 Units, 8 - 4096, 4 - Units
    • Extension

    • 17 units, 18 - 16, 15 - 256,


  • When you are finished don't forget to screenshot your answers to your powerpoint

  • Task 3 - Converting Hexadecimal Click to see more

    What is Hexadecimal?

    As we have previously mentioned our counting system is based on 10's and computer is based upon 0's and 1's.

    So why do we use hexadecimal?


  • Which of the following numbers is easier to remember?
  • 1011 0111
  • B7

  • If you think B7 is easier and more convenient to remember and use, you now understand why some binary is expressed in hexadecimal format. B7 is actually the same value as 1011 0111; however, it is represented as hexadecimal instead of binary.

    Hexadecimal is a base 16 number system: it makes use of 16 numbers. So if we had a creature with 16 fingers, this is how they would count using hexadecimal:

    Decryption
  • This table shows equivalent denary, binary, and hexadecimal values:
  • Binary
  • Hexadecimal is commonly used in computing because it can represent a byte of data with just two characters (instead of eight).
  • Each hexadecimal character represents half a byte, also called a nibble.
  • So, hexadecimal 7D is equivalent to binary 0111 1101.

  • Task 2

  • Click on the Hexadecimal calculator below:


  • Using the calculator to try and create the following base 10 numbers using the base 16 calculator.
    1. 33
    2. 49
    3. 99
    4. 134
    5. 167
    6. 189
    7. 255
    8. 1052


  • When you are finished don't forget to screenshot your answers to your powerpoint

  • Task 4 - From Binary to Hex Click to see more

    Converting from Binary to Hexadecimal

  • If we have the binary 10110111, and we want to convert it to a hexadecimal number, that seems a very difficult task. However it is actually quite simple.
  • Firstly we need to split our binary byte up into two nibbles

    Nibbles are 4 bits or half a byte

  • So our binary number 10110111 becomes :

  • Binary

    Task 3

  • Convert the following binary numbers into hexadecimal using the technique shown above.
    1. 00101001
    2. 10101010
    3. 01011010
    4. 11010101
    5. 01011001
    6. 11100101
    7. 11111010


  • When you are finished don't forget to screenshot your answers to your powerpoint

  • Task 5 - From Hex to Binary Click to see more

    Converting from Hexadecimal to Binary

  • If we want to convert from Hexadecimal to Binary then we simply reverse the proces we used when coverting from Binary to Hexadecimal
  • For example if we have the Hexadecimal number A5 then we split it up like before and turn each digit into a binary nible.

  • So our Hexadecimal number A5 becomes :

  • Binary

    Task 4

  • Convert the following hexadecimal numbers into binary using the technique shown above.
    1. A1
    2. D3
    3. F7
    4. AB
    5. CC
    6. D9
    7. FF


    Extension

  • Convert the following decimal numbers into hexadecimal.
    1. 17
    2. 39
    3. 48
    4. 55
    5. 92
    6. 151
    7. 254
  • Convert the following hexadecimal numbers into decimal.
    1. A2
    2. D4
    3. F3
    4. A9
    5. C1
    6. 9D
    7. EE


  • When you are finished don't forget to screenshot your answers to your powerpoint

  • Task 6 - Binary Tetris Click to see more

    Task: Binary Tetris

    Click on the image below and see how well you can do at Binary Tetris.



    Task 7 - Lesson review Click to see more

    Summing it all up

    Lets look at the learning outcomes and decide which one best describes our current level of understanding :

    Tick the one you feel is closest to your level

    Learning Outcomes I need to learn how to explain why hexadecimal is often used in computer science.

    • I have a basic understanding of how I can explain why hexadecimal is often used in computer science. with a little help from my teacher
    • I can show my teacher that I can explain why hexadecimal is often used in computer science. without their help.
    • I can explain why hexadecimal is often used in computer science. independently and I can also explain it to others and can complete any extension tasks I am given.

    🠜 Now update your learning objectivesClick on the Assessment image

    My Notes: representing_data

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    Task Notes/Comments - Add here Click to see more

    Comments/Notes

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