By Lauren Atkins, Lara Campbell. Faye Denham, and Alice Warne

Binary Numbers were invented by a German man called Gottfried Leibniz. He was born on 1st July 1646 and died on 14th November 1716. Other than being a famous Mathematician, he was also a philosopher and a polymath(a person of great learning in several fields of study).

Leibniz believed that much of human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion.

One of his famous quotes: “For indeed, there is nothing in the intellect which was not in the senses, except the intellect itself. Music is the pleasure the human mind experiences from counting without being aware that it is counting. Nothing exists and nothing happens without a reason why it is so, and not otherwise”.

Francis Bacon

invented a

“bilateral

alphabet code”

that used “A”

and “B” instead

of “0” and “1”.

George Boole

developed a

system to break

any statements

down into binary

numbers.

George BooleFrancis Bacon

Binary numbers are made / put into a computer using a piece of technology called the practical digital circuit design. It is a system that represents signals at discrete levels, using slates which are represented by two voltage levels. In most cases the number of slates is two.

In a common hard drive there is a disc with a magnetic coating, this coating can be manipulated to change its magnetic polarity so it represents either a 1 or a 0 at any given location of the disc.

Binary has changed to be used in everyday items like the computer I'm typing into now. Computers use Binary to detect errors and when something doesn't go with the Binary code its often wrong.

The IPod was invented by many people including: Jon Rubinstein, Jonathan Ive, Tony Faddle, Michael Dhuey but the main overseer is Steve Jobs, the CEO of Apple, and the name was created by Vinnie Chieco. It was created as the other MP3 players where either large and clunky or small and useless.

The first IPod was the first generation of IPod classics and it looked like this:

Information is transferred to iPods using a digital audio format such as MP3 binary code signal which is a series of electronic pulses.

Data is compressed using Lossy compression which takes away some minor details but is not noticeable to the human ear. The bit level will be very different to the original file but when you hear it, it will be indistinguishable from the original.

1 1 0 0 1 0 0 0

0

50

100

150

200

250

Loudness

Electrical digital signals

Analogue signal

The electronic pulses are measured in things like tempo, tone and volume e.g. A digital pulse may measure 26 so this would be 11010 in binary. The codec compresses the information from a CD into binary and then back into audio so we can hear it. It consists of two major parts, the encoder and the decoder. The encoder compresses a file when you load it to your IPod. The decoder decompresses a file when you want to play it.

1 1 0 0 1 0 0 0

0

50

100

150

200

250

Loudness

Electrical digital signals

Analogue signal

Binary is a system of numbers used for various items like computers and iPods. If it was not for binary what I’m using right now wouldn’t work.

Binary affects my iPod by using the binary numbers to compress songs so that over 8000 songs can be stored on a device this small (the same with movies).

So the song I’m playing is in theory made up from numbers!

If the binary were to go wrong something like this would happen.

In iPods you can have 8GB, 16GB, 32GB etc. So that the iPods can fit more songs and apps the iPod software scales it down e.g. “How are you” to “hw r y” by taking away the vowels in the words.

It shortens it down to fit more songs or videos etc in he amount of space you have.

Ipods use binary by using the codec code and uses the information of the songs and turns it back into sound. Digital Music players store music in digital files (binary code). A converter turns digital files into O’s and 1’s and that is how binary fits into your IPod. The compression depends depends on the size of the file.

In binary it can recover information that has been damaged. If a cd has only a couple of scratches, it can be recovered. However, if there is lots of damage to the disk, binary cannot pick up the information.

How to lie and get away with it!!!

To Find Out If To Find Out If You Are Lying You Are Lying Or Not, You Or Not, You Have To Have To Answer These Answer These Simple Simple Questions…Questions…

Pick a number between 1 And Pick a number between 1 And 7…7…

Is Your Number…Is Your Number…

4, 5, 6, 7? Yes/No4, 5, 6, 7? Yes/No

2, 3, 6, 7? Yes/No2, 3, 6, 7? Yes/No

1, 3, 5, 7? Yes/No1, 3, 5, 7? Yes/No

1, 3, 4, 6? Yes/No1, 3, 4, 6? Yes/No

1, 2, 5, 6? Yes/No1, 2, 5, 6? Yes/No

2, 3, 4, 5? Yes/No2, 3, 4, 5? Yes/No

Here is an example . . .

4, 5, 6, 7? no 4, 5, 6, 7? no

2, 3, 6, 7? yes2, 3, 6, 7? yes

1, 3, 5, 7? yes1, 3, 5, 7? yes

1, 3, 4, 6? yes1, 3, 4, 6? yes

1, 2, 5, 6? no1, 2, 5, 6? no

2, 3, 4, 5? yes2, 3, 4, 5? yes

I have thought of a number between 1 and 7 . . .

Now I will answer the questions . . .

My number was…

3!!!!!!!

So, How did we figure it out???

All the ones you said yes to had a three in it!!!!

It’s simple!!!!!

Now you can try it out on your friends!

Hamming Distance…

• The hamming distance was named after Richard Hamming.

• He was an American mathematician.• It is the number which is used to denote the

difference between two binary strings (codes) of equal lengths.

StepsStep 1. Make sure that the two strings are equal lengths. The hamming distance can only be calculated between two strings of equal length.for exampleString 1 : 1001 0100 1101String 2 : 1010 0100 0010

Step 2. Compare the first two bits in each binary string. If they’re the same, record a 0 for that bit. If they are different, record a 1 for that bit. In this case the first bit of both strings is 1. so record a 0 for that first bit.

Steps continued.

Step 3. Compare each bit, and record either a 1 or a 0.String 1 : 1001 0100 1101String 2 : 1010 0100 0010Record : 0011 0000 1111

Step 4. add all the ones and zeros in the record together to get the hamming distance.Hamming distance= 0+0+1+1+0+0+0+0+1+1+1+1= 6

by Maurice Yap, Josh Kilburn, Dan Lowton, Matt Moody, George Cocks and Matt Sayer.

2^62^52^42^32^2

2^12^0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Row of “1”s.

Row of “2”s.

Base 2

Base 3:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100113

399

27278181

2 lines of “1”'s.

2 lines of “3”'s.

Base 4:

4 ^3

4 ^2

4 ^2

4 ^2

4 ^1

4 ^1

4 ^1

4 ^0

4 ^0

4 ^0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 4 0 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

2 lines of “3”'s.

Negative Binary

By Alex Williams, Jack Howson, Andrew Pritchard, Joe Forrest and James

McGregor

How is negative binary represented?

Negative binary looks the same as positive binary, with the only difference being there

value. For instance, 11111000 is 248 in positive binary, but in negative it is -8

Why we chose negative Binary

We chose this topic as we agreed it was interesting and thought that no one else in our

group would think of it

Negative Binary Explained

This difficult BIT OF BINARY IS SIMPLE ONCE YOU GET TO GRIPS WITH IT. Here it is simplified:

1 1 1 1 1 0 0 0

The starting digit (128) The numbers that are subtracted (In

there squared form)

The 0’s can not be subtracted as they have no value

How you know if it is positive or negative

The answer to that is… it doesn't matter. The computer or the machine which is reading the number will see it as for instance 11111000, not as 248 or –8.