Representation of data in computer systems Units and Numbers

Definitions Denary – A system of numbers using ten digits, 0 and 1-9 (also called the base-10 system) Binary – A system of numbers using only two digits, 0 and 1 (also called the base 2-system)

units When you break a computer down into its basic components it is millions of circuits that either allow electricity to flow; or not! These are switches that have either an ON or an OFF This is why everything stored in a computer is as a series of 1s and 0s. This is called BINARY A single 1 or 0 is a binary digit or a BIT for short

Measuring 8 bits = 1 byte 1024 bytes = 1 kilobyte 1024 kilobytes = 1 megabyte 1024 megabytes = 1 gigabyte 1024 gigabytes = 1 terabyte

For you to find out Why isn’t a kilobyte 1000 bytes? Why 1024, how does this number relate to binary? What comes after terabytes?

Counting in Binary When you learn to add denary numbers you learn to carry each group of 10, then each group of 100 etc. For example: 7 + 5 12 Counting in binary is the same except we only have two digits, 1 and 0 so we carry the group of 2. In maths this is called Base 2

Counting to 10 Denary Binary 1 2 10 1 2 10 Notice that we now move to the second column 3 11 One group of 2 plus one unit 4 100 Now we move to the third column 5 101 6 110 7 111 8 1000 Every time we go to the next column it is two times the previous column 9 1001 1010

Counting up to 20 You need to try to count up to 20 using binary I can come round and help and show you some tricks if needed

converting binary numbers The headings double each time (2 base!) For example: How would we convert the following to binary? 111001 128 64 32 16 8 4 2 1 2x2x2x2x2x2x2 2x2x2x2x2x2 2x2x2x2x2 2x2x2x2x 2x2x2 2x2 128 64 32 16 8 4 2 1

converting to denary numbers If we calculated that 11101 was 57 like this: How would we convert the 57 into denary using the same grid? 128 64 32 16 8 4 2 1 128 64 32 16 8 4 2 1

Try these examples 11011 24 1000110 184 128 10111011 100101001 128 64 32 16 8 4 2 1