Mathematics and numeracy - exploring digital devices
We are all familiar with the decimal system of numbers, where we use the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent any number by placing it appropriately in the H, T, or U column:
Let's suppose we had only two digits, 0 and 1. In a similar way, we can represent numbers like this:
Very interesting, but so what?
Well, from a teaching point of view, many learners don’t fully understand how decimal numbers work. Perhaps by asking them to do base 2 arithmetic with ‘easy’ numbers, the structure could be easier to understand and manipulate.
In the ‘real’ world, using binary (base 2) arithmetic enables us to model situations where there are just two possible states, e.g:
- on or off
- smooth or bumpy
- present or absent.
A major application of this occurs in the computer industry. Computers are made up of lots and lots of tiny electronic switches, whose state can be represented by 1 or 0. Each piece of information held by the switch is called a bit (short for Binary digIT).
Using an 8-bit binary number (a byte) gives us 256 combinations of instructions or information which can be stored. Suddenly we are into bigger numbers.
A hard disk on a three-year-old laptop is 55.8 gigabytes, which is small by today’s standards. What does this actually mean, in terms of units of information stored?
‘Giga’ means the original number multiplied by 1 000 000 000, so this computer can hold 5 580 000 000 bytes of information, which is approximately equal to 230 pieces of information.
Why do modern computers have so much more memory? One reason is because we now use them to download and store music which contains a great deal of information.
For our final piece of number crunching, let’s look at a single CD and how it is made:
- An analogue recording is chopped into 44 100 pieces per second, each of which requires 2 bytes to hold the information
- The sound is recorded on two channels
- 44 100 x 2 x 2 bytes so far….per second
- x 60 …………………………..per minute
- x 74 …………………………..for a 74 minute CD
- A total of 783 216 000 bytes, all contained in a spiral 5 km long!
How could you use some of this information in your teaching?
How many mathematical topics could it link to?
What other everyday contexts could you use in your lessons in a similar way?
Further reading (from howstuffworks.com)