Binary Systems

• 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.

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

• 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:

2⁰ = 1

2¹ = 2

• 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.

• Convert:

  1000 1000

  To denary.

• Convert:

  1100 1111

  To denary.

• Convert:

  0010 0100

  To denary.

• 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:

   

• Now let’s calculate 35:

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

   

• Convert:

  28

  To 8-bit binary

• Convert:

  32

  To 8-bit binary

• Convert:

  254

  To 8-bit binary