CS07 : A bit of this and a bit of that

A bit is a really tiny thing. A tiny bit, as it were. Most useful amounts of data storage contain millions, billions or even trillions of bits. However, computer scientists don't like writing long numbers; they use prefix multipliers to group bits together.

We are learning ...
  • About the ways in which binary data is grouped
So that we can ...
  • Describe the bit as the fundamental unit of information
  • State that a group of 8 bits is called a byte
  • State that half a byte is called a nybble
  • State that n bits of information can be configured in / used to represent 2n different values
  • Represent quantities of data in powers of 10 and in powers of 2
    - Base 10 : kilo, mega, giga, tera
    - Base 2 : kibi, mebi, gibi, tebi
  • Discuss the reasons why historically, the terms kilobyte, megabyte, etc have been used when kibibyte, mebibyte, etc are meant - the hard drive problem.

Activity 1  Fundamental measures of data (20)

The fundamental measure of data in a computer system is the bit. Bit stands for binary digit and is given the symbol 'b'. 8 bits make a byte (symbol 'B') and 4 bits make a Nybble (half a byte - lol). A group of bytes is called a word.

Click to enlarge

Task 1.1 History of the Byte
Web browser

Research the history of the byte at Wikipedia. Write down 5 interesting facts in your notes.

OUTCOME : 5 interesting facts about a byte.

Activity 2 Groups of data (85)

Even though we measure storage in bytes (symbol B), the kilobyte (kB) is often used for the base unit of storage in computer systems these days. This is probably because file sizes often do not come in less than a kilobyte any more like they used to in the old days.

Engineers and scientists use 1000 as the base unit of measurement, whereas computer scientists use 1024 as the base because they like working in powers of 2 and 1024 is 210. To avoid confusion, computer scientists have actually come up with a different set of measurements based on 1024, however, virtually everyone apart from computer scientists works with the engineering units based on 1000. 

Unless you buy a new hard drive, this is never really a problem ...

Task 2.1 Denary prefixes
Notebook and pen

Copy and complete
the following table of denary prefixes. Notice that kilo has a lower case 'k' whereas the others are all upper case ...

OUTCOME : Completed table of denary prefixes in your notes.

Remember : kilo is a lowercase 'k' whereas all the other prefixes are uppercase!

If I was a scientist, I'd work in these units. But what do they 'look' like?

Task 2.2 The size of stuff
Web browser

Google's operations are very secretive, but they are thought to be using over 900,000 servers worldwide storing around 15eB (exabytes) of data. There is a great article on XKCD which explains what this actually means. Visit the website and summarise what you have discovered in your notes. Maybe use a few sketches and diagrams to help you.


Investigate 'scale' by visiting Scale of the Universe and spending 10 minutes marvelling at the scale of our universe and also at the unimaginable amount of data held in the just Google's server farms.


OUTCOME : Summary of the XKCD article and maybe a discussion on the scale of the universe?

Computer scientists group in powers of 2 - that's because they are computer scientists. The nearest power of 2 to 1000 is 210 which is 1024 - slightly more than 1000. It's a bit like a bakers dozen is 13 rather than 12 ...

Task 2.3 Binary prefixes
Notebook and pen

Copy and complete
the following table of binary prefixes. Notice that kibi has a lower case 'k' whereas the others are all upper case ...

Now, convert the following prefixed quantities into bytes.
  • 12 kiB
  • 12 MiB
  • 12 GiB
  • 12 TiB
  • 12 PiB
Convert the following byte quantities into the most suitable binary prefixed value.
  • 348 B
  • 28562 B
  • 95738274 B
  • 359105637599 B
  • 978936147582559205 B
Why don't the general public use these prefixes do you think?

OUTCOME : Completed table of binary prefix values plus some super data conversions.

Remember : kibi starts with a lowercase 'k' whereas all the other prefixes start with uppercase!

I remember the order of the colours of the rainbow using this mnemonic ...

 Richard Of York Gave Battle In Vain 

Task 2.4 Mnemonic

In order to remember the order of the prefixes, come up with a mnemonic of your own and write it down in your notes.

OUTCOME : A (clean) mnemonic to help you remember the order of the binary prefixes.

Activity 3 My hard drive is broken (25)

Speaking of hard drives, here is a screen shot of the properties window of my 250GB hard drive which was made by an engineer, not a computer scientist.

Task 3.1 Hard drive capacity

Why is the capacity of my hard drive only 232GB? Have I been robbed? Is some of the storage being used for something else? Read this article on the Seagate website which should help to explain what's going on.

After you have researched the reasons behind this, write at least a paragraph in your notes about what you have found out. You might want to use diagrams to help you with your explanation.

OUTCOME : Written or diagrammatic explanation of the reasons why I've been robbed.

Extension Activities 

Try these ...
  • Automagic spreadsheet data conversion platform

    Create a spreadsheet which will represent a value you supply using each denary prefix and each binary prefix. The spreadsheet should also calculate the percentage difference between the denary prefix value and the binary prefix value.

What's next?

Before you hand your book in for checking, make sure you have completed all the work required and that your book is tidy and organised. Your book will be checked to make sure it is complete and you will be given a spicy grade for effort.