Slides badge

Binary Systems

Learning Intentions

  • Understand how to convert decimal/denary numbers to binary

  • Understand how to convert binary numbers to decimal/denary

Success Criteria

  • I am able to convert between binary and denary

Denary numbers

  • Denary numbers are the numbers we work with every day. Den = 10, in other words we count in tens and have the following numbers available:
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9

  • We use units that we call tens, hundreds, thousands, tens of thousands and so on.

  • We call denary base 10.

Denary numbers

  • For example, the number of 2385 can be broken down like this:

 

 

 

  • Each of these units can also be represented by:
1000s 100s 10s Units
2 3 8 5
103 102 101 100
2 3 8 5

Binary numbers

  • Binary numbers (bi meaning two, e.g. bicycle means two wheels) use just 0s and 1s.
  • They also use placeholders, but not in the same way. Because binary only has a 0 or a 1, binary is what we call base 2.
  • Placeholders are as follows:
23 22 21 20
1 0 1 0

An easier way to figure it out

  • 23 = 8
    22 = 4
    21 = 2
    20 = 1

23 22 21 20
8 4 2 1

Figuring out denary from a binary number

  • Let’s figure out what the binary number 1001 means in denary:

 

   

  • To do this, add each number with a 1 under it together, so 8 + 1. Total is 9. So 1001 = 9.

8 4 2 1
1 0 0 1

Example 1

  • Convert:

    1000 1000

    To denary.

Example 2

  • Convert:

    1100 1111

    To denary.

Example 3

  • Convert:

    0010 0100

    To denary.

Figuring out binary from a denary number

  • Reversing binary to give us a decimal number is a bit trickier. The placeholders are the same and should be put at the top. Hint: the leftmost placeholder should be no bigger than the denary number.

  • Let’s calculate the number 17:

     

16 8 4 2 1
1 0 0 0 1

Denary to binary

  • Now let’s calculate 35:

 

 

 

  • Double check it by adding all the numbers with 1s under them together.

     

32 16 8 4 2 1
1 0 0 0 1 1

Example 1

  • Convert:

    28

    To 8-bit binary

Example 2

  • Convert:

    32

    To 8-bit binary

Example 3

  • Convert:

    254

    To 8-bit binary

Transform to binary:

  1. 33
  2. 19
  3. 28
  4. 73
  5. 109

Task

Transform to denary:

  1. 1011
  2. 10001000
  3. 00011111
  4. 1111
  5. 0110

Work through the calculations on the worksheet.

Presentation Overview
Close
JB
Binary systems
© 2020 - 2024 J Balfour
07:05 | 24-02-2024
Join Live Session
Start Remote
Save Progress
Slideshow Outline
Presenter Mode
Widget Screen
Canvas Controls
Dark Mode
Bold Text
Random Selector
Timer
Volume Meter
Binary Converter
Python Editor
Show Knox 90
Provide Feedback
Help
!
Keywords
    Random selector
    Sections
      Binary conversion
      Denary to binary conversion
      Binary to denary conversion
      Feedback 👍
      Accessibility

      Apply a filter:

      ×
      All slideshow files