Data representation
1.0 -- Binary systems
187 to binary
187-128=59 | 59-32=27 | 27-16=11 | 11-8=3 | 3-2=1 | 1-1=0
128 64 32 16 8 4 2 1
1 0 1 1 1 0 1 1
187 = 10111011
Byte - kilobyte - megabyte - gigabyte - terabyte
For the exams, you can use the 1000 rule as you don’t have a calculator.
Why do computers use binary
● Computer consist of transistors / logic circuits
● that can only store/process data in two states / as high-low / on-off / 1 and 0
255 is the largest number that can be represented with 8 bits!
2.0 -- Hexadecimal
● Closely related to the binary system
, ● Hexadecimal is a base 16 system
● Numbers 0 to 9 and letters A to F are used to represent each hexadecimal digit
● Hexadecimal is used as it’s easier to read and shorter than binary
Hexadecimal to decimal
1. Link each hex digit to 16 to the power of x. 45F -- 4-162, 5-161, F-160
2. You will multiply each number by the 16 to the power of. In order to do this you will
have to convert any letter to its corresponding number.
3. Now create and solve the math equation.
(4 * 162) + (5 * 161) + (15 * 160) = (4 * 256) + (5 * 16) + (15 * 1) = 1024 + 80 + 15 = 1119
45F = 1119
Decimal to hexadecimal
1. Divide the number by 16, keeping track of the remainders
2. Keep doing this until you get to a number less than 16
3. Take the remainders from last to first and translate them to Hexadecimal.
Binary to hexadecimal
1. Divide the binary into nibbles (4 bits)
2. Find the decimal value of each nibble.
3. Find the hexadecimal value of that decimal value
,And back
1. Find the decimal value of each character
2. Find the binary value of that decimal value.
Benefits of hexadecimal Source
● Easier/faster to understand (read and write)
● Easier/faster to debug
● Takes up less screen/display space
● Less chance of making an error
Uses Source
● Media Access Control (MAC) addresses
● Assembly language
● Error codes. Hexadecimal can be used for shorter error messages.
● Locations in memory
● Defining colours in Hypertext Markup Language (HTML)
3.2 -- moved to 1.5
3.3 -- File Formats
File Type File Format
, Sound .mp3 .wav .mid .flac .aif
Text .doc .docx .rtf .txt .pdf
Pictures .jpeg .gif .png .bmp
Video .mp4 .flv .wmv
MIDI
Musical Instrument Digital Interface
● Stores the notes played and not the sound
● Can edit individual notes
● Can be a compressed format
● Recorded using a musical instrument
● Contains instructions/commands for digital instruments
MP3
● Contains actual sound
● Uses lossy compression
● Recorded using microphone
MP4
● Contains video AND audio
● Lossy compression
JPEG
● Contains digital images
● Lossy compression
3.4 -- Data compression
Data Compression - Computer Science GCSE GURU
Lossy data compression Source (ctrl+f “lossy”)
● A way to compress/reduce the size of a file by using an algorithm that permanently
removes redundant/useless information. This reduction should not be very noticeable.
● Examples of things lossy compression would reduce would include:
○ Image resolution
○ Image colour depth/range of pixels
○ Sound sample rate
○ Background noise
● Can be applied to music, video, or picture files, but NOT for text files or spreadsheets
Lossless data compression
● A way to compress/reduce the size of a file without losing any data
1.0 -- Binary systems
187 to binary
187-128=59 | 59-32=27 | 27-16=11 | 11-8=3 | 3-2=1 | 1-1=0
128 64 32 16 8 4 2 1
1 0 1 1 1 0 1 1
187 = 10111011
Byte - kilobyte - megabyte - gigabyte - terabyte
For the exams, you can use the 1000 rule as you don’t have a calculator.
Why do computers use binary
● Computer consist of transistors / logic circuits
● that can only store/process data in two states / as high-low / on-off / 1 and 0
255 is the largest number that can be represented with 8 bits!
2.0 -- Hexadecimal
● Closely related to the binary system
, ● Hexadecimal is a base 16 system
● Numbers 0 to 9 and letters A to F are used to represent each hexadecimal digit
● Hexadecimal is used as it’s easier to read and shorter than binary
Hexadecimal to decimal
1. Link each hex digit to 16 to the power of x. 45F -- 4-162, 5-161, F-160
2. You will multiply each number by the 16 to the power of. In order to do this you will
have to convert any letter to its corresponding number.
3. Now create and solve the math equation.
(4 * 162) + (5 * 161) + (15 * 160) = (4 * 256) + (5 * 16) + (15 * 1) = 1024 + 80 + 15 = 1119
45F = 1119
Decimal to hexadecimal
1. Divide the number by 16, keeping track of the remainders
2. Keep doing this until you get to a number less than 16
3. Take the remainders from last to first and translate them to Hexadecimal.
Binary to hexadecimal
1. Divide the binary into nibbles (4 bits)
2. Find the decimal value of each nibble.
3. Find the hexadecimal value of that decimal value
,And back
1. Find the decimal value of each character
2. Find the binary value of that decimal value.
Benefits of hexadecimal Source
● Easier/faster to understand (read and write)
● Easier/faster to debug
● Takes up less screen/display space
● Less chance of making an error
Uses Source
● Media Access Control (MAC) addresses
● Assembly language
● Error codes. Hexadecimal can be used for shorter error messages.
● Locations in memory
● Defining colours in Hypertext Markup Language (HTML)
3.2 -- moved to 1.5
3.3 -- File Formats
File Type File Format
, Sound .mp3 .wav .mid .flac .aif
Text .doc .docx .rtf .txt .pdf
Pictures .jpeg .gif .png .bmp
Video .mp4 .flv .wmv
MIDI
Musical Instrument Digital Interface
● Stores the notes played and not the sound
● Can edit individual notes
● Can be a compressed format
● Recorded using a musical instrument
● Contains instructions/commands for digital instruments
MP3
● Contains actual sound
● Uses lossy compression
● Recorded using microphone
MP4
● Contains video AND audio
● Lossy compression
JPEG
● Contains digital images
● Lossy compression
3.4 -- Data compression
Data Compression - Computer Science GCSE GURU
Lossy data compression Source (ctrl+f “lossy”)
● A way to compress/reduce the size of a file by using an algorithm that permanently
removes redundant/useless information. This reduction should not be very noticeable.
● Examples of things lossy compression would reduce would include:
○ Image resolution
○ Image colour depth/range of pixels
○ Sound sample rate
○ Background noise
● Can be applied to music, video, or picture files, but NOT for text files or spreadsheets
Lossless data compression
● A way to compress/reduce the size of a file without losing any data
