Section 3 - Fundamentals of Data Representation

What does ASCII stand for?

American Standard Code for Information Interchange

What does ASCII do?

It allows every character to be represented as a 7-bit binary pattern, allowing 128 different characters to be represented

Eg. A is represented by 1000001, same binary code as the decimal no. 6

What are the pseudocode funtions for casting to and from ASCII?

"CHAR_TO_CODE(""A"") evaluates to 65
CODE_TO_CHAR(66) evaluates to ""B"""

What are the python functions for casting to and from ASCII?

"chr(66) will return the character represented by 66
ord(""A"") will return the code that represents ""A"""

In ASCII code, is a lowercase letter worth more or less than an uppercase one?

"More ""a"" > ""A"""

In ASCII code, is a letter further in the alphabet worth more or less than an earlier one?

"More

""Z"" > ""A"""

How do you work out the binary and ASCII codes for a letter?

"64 32 | 16 8 4 2 1
1 0 | 0 0 0 0 1 Putting 10 at the start means it is an uppercase letter, putting 11 means it is a lowercase letter
1 1 | 0 0 0 0 1

The numbers to the right of the line are always the same - they always add up to the position of the letter in the alphabet

All the numbers (on both sides of the line) added together will make the ASCII code of that letter

""A"" = 1000001 = 64 + 1 = 65
""a"" = 1100001 = 64 + 32 + 1 = 97"

How do computers work?

By turning switches on/off to allow electricity to flow or not

What happens if a switch is on?

It's closed and electricity flows (state of 1)

What happens if a switch is off?

It's open and no current will flow (state of 0)

What are the 2 states a switch can be in?

1 or 0 - binary

What is a single 0/1 called?

A bit (Binary digIT)

What is base 10?

Denary/decimal

As we go up in 10s when counting

1s --> 10s ----> 100s

What is 1 byte?

8 bits

What is a byte?

The smallest addressable unit of memory in a computer (8 bits)

What is a nibble?

4 bits (half a byte)

What is a kilobyte (kB)?

1,000 bytes (10^3)

What is a megabyte (MB)?

1,000,000 bytes (10^6) = (1,000KB)

What is a gigabyte (GB)?

1,000,000,000 bytes (10^9) = 1,000MB

What is a terabyte (TB)?

1,000,000,000,000 bytes (10^12) = 1,000GB

What is a petabyte (PB)?

1,000,000,000,000,000 bytes (10^15) = 1,000TB

How do you convert from binary to denary?

128     64     32     16    8    4     2   1

If there is a 1 in the column, then the number above is added to the total

If there is a 0, then add nothing

Convert 67 into binary

01000011

Convert 01100001 into denary

97

What does internal memory often use instead of MB,KB,etc...

Powers of 2:

KiB (kibibyte), MiB (mebibyte), GiB (gigibyte)

What is a kibibyte?

2^10 = 1,024 bytes

What is a mebibyte?

2^20 = 1,048,576 bytes

What is a gibibyte?

2^30 =  1,073,741,824 bytes

What do computers use the binary system for?

To store numbers and perform binary arithmetic and logic operations

What is the memory size of secondary storage systems commonly measured in now?

Terabytes (TB)

The more bits we use...

The more possible values they can store

eg. 2 bits can store 4 possible values, while 3 bits can store 8 possible values

What is the no. of different values that can be represented in n bits?

2^n

Eg. to represent 17 values, you will need 5 bits (2^5) - (2^4 is too little)

What is the highest no. we can store in n bits?

2^n - 1

(the number of different values that can be represented - 1)

How many bits would be required to encode every letter of te alphabet in upper & lower case?

52 letters ---> 2^6 = 64

6 bits needed

How many different colours could be stored if we encoded each colour in 8 bits?

2^8 = 256 colours

How many bits would we need to store each pixel if we needed 16 million different possible colours?

2^n = 16,000,000+

n = 24 bits

If every colours is represented by a total of 24 bits, how many different colurs can be stored in this way?

2^24 colours

What are the rules of binary addition?
1+0=
0+1=
1+1=
1+1+1=

1+0=1
0+1=1
1+1= Write 0, carry 1
1+1+1= Write 1, carry 1

""

What happens if you add 2 binary numbers together that result in a number bigger than 255?

It will need 9 bits - causing overflow

What is overflow?

A computer stores things in memory with a finite amount of space

If you can't represent this no. in that amount of space, then overflow accurs

(Eg. if u try to use 8 bits to store a 9 bit - overflow error as 9th bit doesn't fit in 1 byte allocation)

How do you double a binary number?

"Shift the bits 1 space to the left (a bit may ""fall off"" the end of the byte)

Put a 0 in empty spaces"

"Multiply this binary number by 2

How can you check binary arithmetic?

Convert into denary

How do you divide a binary number by 2?

"Shift all the bits 1 space to the right (a bit may ""fall off"" the end of the byte)

Fill any gaps with a 0"

"Divide this binary number by 2:
"

""

What is the smallest value you can hold in a nibble?

0000

What is the largest value you can hold in a nibble?

1111

What is hexadecimal?

Base 16 

What is base 16?

A way of representing the decimal values 0-15 with a single digit

How is 0-15 represented in a single digit if we only have 0-9 numbers?

We use letters A-F to get up to 15

How do you convert from hexadecimal to denary?

Take the first number/letter and multiply it by 16, then add on the second number/letter

What is A-F in denary?

10,11,12,13,14,15

Convert 10 in hex to denary

(1 x 16) + 0 = 16

15 is the biggest number u can have with 4 bites - 16 is 1 group of 16 and no units

Why do we use hex and not double digits in denary?

We needed to find a way to represent every group of 4 bits with a single digit (the largest number that u can store in 4 bits is 15 so we need to go up to 15)

Convert A7 to denary

A = 10

(10 x 16) + 7 = 167

How do you convert from binary to hexadecimal?

Try 0101 1100

"If it is 8 bits, split into 2 nibbles

Then convert each nibble to denary and substitute for the hex values

Eg.

0101 = 5    1100 = 12

5 in denary = 5 in hex

12 in denary = C in hex

Therefore it is 5C

"

How do you convert from decima to hexadecimal?

Try 182

Divide the decimal no. by 16

Convert this result into hex

Then take the remainder and convert into hex

Eg. 182

182/16 = 11 remainder 6

11 = B in hex

6 = 6 in hex

Therefore 182 = B6

How do you convert from hexadecimal to binary? Try A7

Convert each hex digit into a nibble

Eg. A = 10

A ---> 1010
7 ----> 0111
A7 = 10100111

What are the advantages of hexadecimal?

Hex is used because it is quicker to write, quicker to type, and
quicker to decode than binary. It also takes less space on the
page when written down

What is hex used for?

Picking numbers for a graphic

In assembly language instructions (eg. ADD & 4F3A)

When using hex, remember...

YOUR COMPUTER DOES NOT USE HEX, IT IS STILL STORED AS BINARY AND TAKES UP THE SAME AMOUNT OF SPACE IN MEMORY

What does ASCII stand for?

American Standard Code for information Interchange

How many bits does ASCII use per character?

7

How many different characters can be represented in the ASCII character set?

128 characters (0-127) (2^n - 2^7)

How are the character codes grouped and run?

"In sequence

(eg. if 'A' is 65, then 'C' must be 67)
(eg. since ""7"" is 55, ""9"" must be 57)"

"""7"" < ""9"" or ""7"" > ""9""?"

"""7"" < ""9"""

Why can't you calculate with numbers that are input as strings?

"The ASCII code value for a number is different from the pure binary value of that number

eg. ""5"" = 0011 0101 but 5 = 0000 0101"

How many bits does the extended ASCII character set use?
How many characters can it represent?

8 bits (so can represent 256 characters in total)

What do the extra characters in extended ASCII do?

They're used for characters from foreign languages and special symbols

What is unicode?

A character set which is the new standard for representing the characters of all the languages of the world

How many bits does unicode use per character?

Between 8, 16 or 32 bits per character

What are the advantages of unicode?

- Provides a unique standard for all the world's writing systems
- Allows for mulilingual text in any language

Why is unicode better than ASCII?

It can represent many more unique characters than ASCII because of the large no. of bits avaialble to store a character code

Does Unicode use any of the same codes as ASCII?

Yes, up to 127

What is a character set?

A character set is a list of characters that are recognised by the computer, along with the binary codes to represent them

Where do the ASCII capital letters start?

At 65

Where do the ASCII lowercase letters start?

At 97

What do you do to convert from upper to lowercase in ascii?

Add 32 to the ASCII code

If you are ever asked to calculate how many bits are needed to store a sentence in ASCII...

multiply the number of characters (including spaces) by 7

Although ASCII uses 7 bits per character....

The computer will use a full byte to store each character.  

For this reason, the size of a text file IN REAL LIFE (NOT FOR THE EXAM) will be the same as the number of characters contained within it.  Don’t forget to include spaces in the count though!

Which characters are the same in ASCII and Unicode?

For compatibility reasons, and because ASCII came first, the first 128 UNICODE characters are the same as the ASCII characters.

Why is Unicode used?

Unicode is used because it enables the characters from all the worlds writing systems to be encoded

What is the disadvantage of Unicode?

It has a disadvantage in that files that include Unicode text will be bigger than files using ASCII. This is because UNICODE uses more bits for each character.

What is a pixel (picture element)?

The single point in an image, which can have its colour set independently

What is a bitmap?

A set of bits that represents a graphical image, which each bit (or group of bits) corresponding to a pixel in the image

Photos taken with digital cameras are...

Bitmap images

(some bitmap images have the file extension bmp)

What is the resolution of an image?

The number of pizels in each dimension that can be displayed (usally represented as 2 numbers eg. 600 x 400)

For printers, the resolution is..

The number of pixels or dots per square inch that cna be printed (dpi)

What is the colour depth?

The number of bits used to encode the colour of each pizel

A higher colour depth will enable...

pictures with a larger range of colours to be encoded

How do you calculate the number of colours that can be represented with the colour depth?

"2**n

Eg. for up to:
2 colours (2^1)

What is each pixel represented by?

A binary code to represent the colour of the pixel

What is metadata?

The information about the image which is encoded within the bitmap file

What is included in the metadata?

- File type, date created, author

- Height and width
- Resolution
- Colour depth

If only 1 bit is used to encode each pixel...

The only colours will be black or white

The number of bits used to encode the colour of each pixel...

detemines the quality of the image

How is black/white represented in a bit?

1 (pixel on) for white and 0 (pixel off) for black

What is true colour?

The term used to describe a colour depth of 24 bits - giving 2^24 different colours

How many bits used to represent each component of the colour in true colour?

1 byte (8 bits) is used to represent each of the RGB components of the colour