How does binary work?

Like the decimal system that we all use on a daily basis, binary notation is just another way of writing down numbers. To get the idea of how it works across, I'll start off by briefly explaining how the decimal number system works: 

How to read decimal numbers

31

The number above is 'thirty-one'. You know that because you've been brought up to count using the decimal number system. We, as a developed society, use it to a large extent not only because there are some nice, easy to remember patterns that make themselves present with a decimal number system, but because that's what our parents used, and their parents, and their parents...

How does it work?
The number system we're familiar with uses ten 'bases' - the symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0 - displayed in a place value system. That means that where we put them in relation to each other is important. We know that '31' means 'thirty-one' because written like that the 3 represents 'three tens' and the 1 represents 'one unit'. Put together, three tens and one unit make thirty one (of whatever we're counting) altogether.

We can represent ever bigger numbers by adding in more columns to the left- the next one, for example, allows us to say how many hundreds we want (0 - 9), the one after that describes how many thousands there are, and so on for ever and ever and ever, if we wanted to.

That's a crash course in the decimal "base ten" number system- remember that's the one you use every day. On to binary.

How to read binary numbers

11111

The number above is also 'thirty-one', or rather it represents the same amount as the number 31 does in the decimal number system.

How does it work?
The binary system works in a similar way to the decimal one, except it uses only two 'bases': 0 and 1 (i.e. there are no 2s, 3s, 4s, 5s, etc). Instead of each digit telling us how many 'ones', 'tens', 'hundreds', etc are in the number, the columns are labelled in a different way. The first column (starting from the right) is still 'units' (or 'ones'), but the next one to the left now represents how many twos we want in our number. The one after that is how many fours, and then it's how many eights. Can you see the pattern? Each column (as we move to the left) represents double the value of the one before it, so:

11111 means:

One 'sixteen', one 'eight', one 'four', one 'two' and one 'one'. Added together this makes thirty-one.

Another example, on binary day:
Today's date is the tenth of October, 2010, or 10 10 10, and is being called 'binary day' for fairly obvious reasons.

so as a binary number, 101010 means:

One 'thirty-two', no 'sixteen', one 'eight', no 'four', one 'two' and no 'one'. Add the thirty-two, eight and two together and you get:

42

Maths tutoring now available!

Just a quick note to say that I'm now offering private mathematics tuition, primarily to people in the Kettering area of Northamptonshire but if you're further away and still want to hire me get in touch and I'll see what I can do.

I'm offering sessions on anything up to GCSE level at the moment, whether you're at school or a more mature student. Get in touch and we can discuss your needs, whatever they are. My prices start at £25 per hour (but may be more if you want me to travel further).

I have profiles on the following tutoring websites:
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Feel free to get in touch through any of those, or use the contact me page on this site.

Why me?
I've got experience and understanding: when I first started out in the teaching business I was a teaching assistant in a local primary school. I know my stuff and I got on really well with the kids so I started working with individuals and small groups, sometimes helping those who were struggling to catch up, sometimes taking the more confident kids and pushing them further. I earned myself a good reference from the head teacher and started a PGCE* course, training to teach mathematics at secondary level. I've been teaching maths in a local secondary school ever since.
I've also worked in industry, fast food, a mobile telephones shop and the job centre, so I do have some experience of the real world outside of a classroom!
In terms of understanding, I earned myself a BSc in Mathematics with Astronomy from the University of Leicester. Maths teachers who actually have a maths degree are not as common as you might think.

I know my stuff, and if you're the kind of person who wants to learn and is willing to put the time and effort in, then I am as well.

• Maybe you've had some time off school and want to catch up with what your class has been doing in the mean time: I can help.
• Maybe you're headed for a B in your GCSE but you really want that grade A: I can help.
• Maybe you're not all that keen on maths but you know the value of getting that all important C and want to put that little extra in to get it, if only you can find someone to guide you: I can help.

I don't care if you're eight or eighty: if you want to improve your game in maths: I can help.

Who am I?
Why would you want to hire anybody without knowing whether you were going to get on with them? If I tell you a bit about me then hopefully you'll see that we can get on and have a bit of fun as well as learning some maths.

First and foremost, I'm a geek (but don't change channel just yet...). I'm into most things science related which is where my love of maths comes from: a good understanding of maths can help you to understand and explain pretty much anything else in a bit more depth. I love learning new things and almost equally love passing on the things I've learnt to anyone who wants to learn too. I'm especially interested in astronomy**, which is an incredibly mathematical science, and run a blog in which I answer questions on related issues. Head over to Blogstronomy and have a look!

I don't just do maths and science, though. I also play guitar, sometimes in a band that plays classic rock covers (and the odd slightly more modern number). I have long hair and am fond of leather jackets and a decent Status Quo riff, but I went to see - and thoroughly enjoyed - the Hairspray musical recently, and I'm looking forward to the 25^th anniversary showing of Les Miserables: my tastes are varied.

I'm young (I'll hit 28 next week, but you don't have to get me a card), enthusiastic, flexible and committed to helping you hit the targets that you set for yourself.

If you have any questions about me, maths or what I offer, or would like to enlist my services, please read the new tutoring page on this site, and then get in touch.

I've been given a lot of advice and guidance by Colin over at Flying Colours Maths who has also listed me as part of his expanding empire.




* PGCE stands for Post-Graduate Certificate of Education - it's the most popular route for gaining Qualified Teacher Status in the UK.
** Not to be confused with astrology..,