Why Binary and not Decimal?

Everyone’s familiar with Decimal. It’s the number system we all use every day – and for good reason – we have 10 fingers and 10 toes. For a humans it just makes sense.

When working with electronics however, 10 different states isn’t easy to represent, especially when working with low voltages. Noise is  huge problem, as is deciding which voltage represents each state. Try to implement a digital circuit which uses more than 2 states and you’ll get yourself into a whole lot of bother. Binary is perfect for digital circuits, very low voltages correspond to 0 and high voltages 1.

In this graph, anything above the top dotted line represents a 1 and everything below the bottom line represents a 0.

The use of binary makes circuits and hardware much more stable and less prone to noise. It makes them simpler too, without the use of binary, digital circuits would be nowhere near as advanced as they are today.

We can use very simple building blocks with simple rules to take billions of  transistors and create insanely powerful hardware that’s fast, stable and cheap.

How do I convert from Decimal to Binary?

So lets recap. Binary is a base-2 number system, that means it only has 2 symbols, 1 and 0, to represent every number. This sounds insane but its actually very simple and doing maths with it is similar and can be done in the same way you were first taught how to add and subtract decimal numbers when you were young.

Let’s start of by converting from a decimal number, such as 14, to binary. It’s actually fairly simple. Binary is read from right to left and every digit represent a power of 2. You’re probably familiar with the powers of 2, they’re very recognisable and crop up all the time in computers, the first few are 1, 2, 4, 8, 16, 32, 64 and 128.

There are a number of ways to convert from decimal to binary, some are faster than others but they all work. We’ll start with the simplest one first. It involves dividing the number by 2 and taking the remainder as the binary digit. Every time we divide by 2 we are increasing the power of 2. This method is best given as an example:

MATHS                           BINARY NUMBER SO FAR
14 ÷ 2 = 7 remainder 0          0
 7 ÷ 2 = 3 remainder 1          10
 3 ÷ 2 = 1 remainder 1          110
 1 ÷ 2 = 0 remainder 1          1110

So starting with 14 and dividing by 2 we get 7 with 0 remaining. It the remainder that is important here as it’s our binary digit. Note it down and repeat the steps again with 7. This time we have a remainder of 1. This is our second binary digit and it goes to the left of the 0 giving us 10. Remember, when using binary we read and write from right to left. Doing the same again with 3 gives us another 1 (110) and finally repeating the process again gives us 1 which means that 14 in binary is 1110.

Converting from Binary to Decimal

Converting from binary to decimal is very simple. My favorite method for doing so is to write out the binary number and above each digit write the powers of 2. I then sum all of the powers which have a 1 below them to get the decimal value.

Powers of 2:   16   8   4   2   1
Binary:         1   1   0   0   1
Decimal:       16 + 8 + 0 + 0 + 1 = 25

We can use this to check that the binary value we got for 14 earlier is correct.

Powers of 2:   8   4   2   1
Binary:        1   1   1   0
Decimal:       8 + 4 + 2 + 0 = 14

I’ve included a table with the decimal numbers from 0 to 31 and their binary counterparts below.

Binary    Decimal   |   Binary    Decimal
000000       0      |   010000      16
000001       1      |   010001      17
000010       2      |   010010      18
000011       3      |   010011      19
000100       4      |   010100      20
000101       5      |   010101      21
000110       6      |   010110      22
000111       7      |   010111      23
001000       8      |   011000      24
001001       9      |   011001      25
001010      10      |   011010      26
001011      11      |   011011      27
001100      12      |   011100      28
001101      13      |   011101      29
001110      14      |   011110      30
001111      15      |   011111      31

This is an account of my thoughts about 1st year and will hopefully prove useful to anyone starting university soon.

Living away from home

University was exactly what I expected and hoped for. It gave me much more freedom, not just in terms of my eduction but my life too. Living away from home has been the biggest change and although I do miss my family, it’s been the most positive too.

I’m not talking about the ability to do whatever I want or stay out as late as I want – my parents have always been very trusting and relaxed when it came to what I did. Being forced to be independent and do things for myself made me a more organised person. It increased my confidence and made me even more determined to succeed.

Student Halls

If you’re living in Halls, or even just a student flat, you’ll become accustom to all of these:

• Alcohol
• Drugs
• Dirt
• Noise

You’ll meet lots of people you can’t stand too. I’m not a big drinker. I’ve never done drugs. I can’t sleep with lots of noise and I like things to be clean and tidy. For anyone like me student halls sounds like a nightmare, but you know what? I loved every minute of it!

You’ll meet lots of people. Some of them you’ll hate. Others you’ll get on with and, if you’re lucky, you might even find someone you love. Drink, drugs, noise and dirt are all part of student life. Alcohol will be all around you almost every day. You don’t have to drink it if you don’t want to. I didn’t encounter anyone trying to sell me drugs, although there are obviously people who are on them.

Noise and dirt, on the other hand, are something you’ll just have to get used to. Most people will be living away from home for the first time and some of them won’t remember to shower every day or, in some cases, every week. Keeping the kitchen & bathroom clean, washing clothes and changing the bed just proves too much for some people. Keep yourself clean and tidy and with a bit of luck the people around you will do the same. A little push in the right direction here and there – a comment about the pile of unwashed dishes at the sink or how messy the bathroom is can help but it doesn’t always work – they’ll quite possibly hate you because of it – but sometimes (and more often than not) they’ll apologise and clear up their mess.

“Mum, what’s for dinner?”

It’s a line that I got far too used to blurting out at home. For my first night in student halls, when my tummy started to rumble, I was left thinking: “What the hell do I do now?”. I could cook my own food easy enough – that wasn’t my problem. It was the daunting task of making myself 3 meals per day, every day and doing the dishes afterwards. On top of all that, I actually had to go out and buy the food and ingredients too!

Somehow I survived though.

Feeding yourself isn’t as difficult as you’d think and after a while you get used to it. Depending on how brave you are (and your budget) you might even start to investigate and try some more adventurous dishes than pasta or baked beans – the hardest part is usually just getting together the ingredients and equipment you need.

Lectures, labs, workshops

Lectures won’t teach you everything, in fact they won’t teach you very much at all. The real learning is done in preparing for, and during, labs and workshops (I’m talking as a science and maths student here, other subject areas, such as English may be different).

I’m not saying that you shouldn’t go to lectures, they are still very important and you should attend them as often as possible. However, you wont fail the year because you missed one or two lectures. What they do provide you with is all the information you need to complete the labs, workshops and coursework. The notes you take in lectures are the basis of your learning. Don’t neglect lectures, you wont know what to do in labs, miss workshops and when exam time comes running along you’ll find yourself begging others for notes.

Labs are what taught me the most. Preparation for labs is important. Before a Computer Science lab I generally complete most of, if not all of, the set work for that lab. Why? Because labs are where you have most access to help. Work out problems before you go, find your weaknesses. You can ask as many question as you need and get help, not only from your tutor, but from the other people in your lab too.

Workshops are small tests done either at home or, for the majority, in class. They count for a percentage of your overall grade and are definatly work working for. Consider these as a chance to bump up your grade without too much work. They serve as great examples of the sort of thing you can expect in the actual exam.

It’s lots of work

Student life really is a lot of work. University is hard and if you want an easy ride then it’s not the place to be. You can do nothing all year, skip all your lectures, miss workshops and labs, get drunk every night of the week and sleep during the day – you’ll have the time of your life – but you’ll probably fail.

It’s ok to have fun, go out drinking and miss a few lectures here and there. All work and no play would make life suck. It’s not, however, a good idea to treat every week like its freshers week.

Good luck

That’s all I have to say. I loved first year and if you’re about to start University I hope you do to.

I hope to write up a review of 1st Year Computer Science at Glasgow soon and go into some detail about the course but for now I’m going to leave you with a picture of a really cute cat I found.

As you can see, I decided to go ahead with it.

I’ll be posting about Project Euler when I find time and hope to write about my first year at the University of Glasgow (hint: I loved it) sometime soon.

I hope to be able to showcase some of my web design work here too. I’m always looking to earn a bit of extra money doing web design or programming work so if you think you have something to offer then please get in touch.