Watch this video for an explanation of binary

Computers are basically a collection of billions of switches. The switches can be on or off represented in binary. Binary is a number system represented by two numerical values:

All data and program instructions are stored as binary strings in a computer.

Place Value

In number systems, a digit’s place value determines how much it contributes to the final total

With decimal numbers (denary), we use base 10, with 10 values (0-9) for each digit

(2x100)+(3x10)+ 5x1) = 200 + 30 + 5 = 235

With binary, we use base 2, with 2 values (0 and 1) for each digit

(1x4) + (0x2) + (1x1) = 4 + 0 +1 = 5

Example

Calculate the Denary (Base 10) value of 10101101

(1x128)+(1x32)+(1x8)+(1x4)+(1x1) =128+32+8+4+1 = 173

Calculate the Binary equivalent of 43

Is 43> 128? - No so 0 goes under 128

Is 43 >64? - No so 0 goes under 64

Is 43>32? - Yes so 1 goes under 32. 43-32 = 11

Is 11>16? - No so 0 goes under 16

Is 11>8? - Yes so 1 goes under 8. 11-8 = 3

Is 3>4? No so 0 goes under 4

Is 3>2? - Yes so 1 goes under 2. 3-2 =1

1 left over so 1 goes under 1

So 43 converts to 00101011 in binary

Here are some workbooks for you to try out

Download this Spreadsheet for some further revision exercises.