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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.

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Binary systems
© 2020 - 2024 J Balfour
12:59 | 29-04-2024
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