Transcript Slide 1

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
George Boole
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 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.
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.
Analogue signal
Loudness
250
200
150
100
50
0
Electrical digital signals
1
1
0
0
1
0
0
0
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.
Loudness
Analogue signal
250
200
150
100
50
0
Electrical digital signals
1
1
0
0
1
0
0
0
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
You Are Lying Or
Not, You Have
To Answer These
Simple
Questions…
Pick a number between 1 And 7…
Is Your Number…
4, 5, 6, 7?
Yes/No
2, 3, 6, 7?
Yes/No
1, 3, 5, 7?
Yes/No
1, 3, 4, 6?
Yes/No
1, 2, 5, 6?
Yes/No
2, 3, 4, 5?
Yes/No
Here is an example . . .
I have thought of a number between 1 and 7 . . .
Now I will answer the questions . . .
4, 5, 6, 7?
no
2, 3, 6, 7?
yes
1, 3, 5, 7?
yes
1, 3, 4, 6?
yes
1, 2, 5, 6?
no
2, 3, 4, 5?
yes
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.
Steps
Step 1. Make sure that the two strings are equal
lengths. The hamming distance can only be
calculated between two strings of equal length.
for example
String 1 : 1001 0100 1101
String 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 1101
String 2 : 1010 0100 0010
Record : 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.
Base 2
2^6
2^5
2^4
2^3
2^2
2^1
2^0
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 5
Row of “1”s.
Row of “2”s.
Base 3:
2 lines of “1”'s.
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
1
1
3
3
9
9
27
27
81
81
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
2 lines of “3”'s.
39
40
41
42
43
44
45
46
47
48
49
5
Negative Binary
By Alex Williams, Jack Howson,
Andrew Pritchard, Joe Forrest and
James McGregor
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
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
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 0’s can
not be
subtracted
as they have
no value
The numbers that are subtracted
(In there squared form)
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.