Section 7 - Data Representation

Section 7 - Data Representation

1. Logic Gates apply Boolean Operations to inputs

   • Logic gates receive binary data, apply a boolean operation and then output a binary result
   • Each type of logic gate is represented by a different symbol
     • NOT Gate
       • • Take 1 input and gives a single output
           • The output will be the opposite of what the input is, is the input is 1 the output is 0, and visa versa
     • AND Gate
       • • Takes two inputs and gives one output
           • Both inputs must be 1 for the output to be 1, otherwise the output is 0
     • OR Gate
       • • Takes to inputs and gives one output
           • If one or more inputs are 1, the output is 1, otherwise the output is 0
   • Each type of logic gate will have its corresponding truth table

2. Logic Gates can be combined to make more complex operations

   • And example of this is above

3. Units

   • Bits are the smallest measure of data
     • All data we want to process, it must be converted into binary code
       • Each 1 or 0 is a bit (binary digit)
   • Units and their sizes:
   • Parity bits are used to check for errors
     • Check digits check that data has been entered and read correctly
       • Check digits are added to the end of numbers and calculated using other digits within the number
       • If the check digit is correct when the data is read, then it's likely that the data has been entered and read correctly
     • For binary data, the check digit is called a parity bit
       • These can be even and odd
       • Even
         • An even parity bit is added to make a binary string have an even number of 1s
       • Odd
         • An odd parity bit is added to make a binary string have an odd number of 1's

4. Binary Numbers

   • Adding
     • 1 + 1 = 10
     • 1 + 0 = 1
     • 0 + 0 = 0
     • 1 + 1 + 1 = 11
   • Overflow errors
     • An overflow error will occur if a binary numbwe has too many bits
       • For example if a binary addition gave a 9-bit answer this would be overflow
         • This is because a byte only contains 8-bits not 9
     • Computers usually deal with these by storing them elsewhere
     • Overflow flags are used to show that an overflow error has occurred
   • Binary Shifts
     • This can multiply a binary number by 2 (or divide it)
     • Gaps at the beginning or end are filled in with 0s
     • Left shifts
       • Multiplies a binary number
         • The number is doubled
     • Right shifts
       • Divides a binary number
         • This will half the number

5. Hexadecimal Numbers

   • Hexadecimal uses 16 different digits
   • A single hex character can represent any denary number from 0-15

6. Characters

   • Binary can represent characters
     • Alphanumeric characters are used to make words and strings
       • These include Upper and lowercase letters, the digits 0 - 9 and symbols
     • Computers cannot process these characters as they only process binary code
       • To convert these characters they use character sets
         • Character Sets
           • Character sets are collections of characters that a computer recognises from their binary representation
             • When a button is pressed on your keyboard a binary signal is sent to the computer telling it which key was pressed
           • Characters also contain special characters in which do certain commands e.g. space, delete
   • The number of bits needed is based on the character set
     • ASCII
       • Most commonly used character set in the English speaking world
       • Each ASCII character has its own 7-bit binary code
         • This means it can represent 128 different characters
           • This includes all the letters in the English Alphabet, numbers, symbols and commands
     • Extended ASCII
       • Each Extended ASCII character has its own 8-bit binary code
         • This allows it to have 256 different characters
           • The first 128 characters are in the same order as normal ASCII
       • Useful for many European languages like French and German which include accents on vowels
     • Unicode
       • Comes in several different forms and tries to cover every character written
         • Covers all major languages, even ones like Greek, Russian and Chinese
       • It's most common form is as 16-bit or 32-bit binary code

7. Storing Images

   • Images are stores as Pixels
     • The type of image that is most often used are called bitmap images
       • These are mainly used for photos
   • The colour of the pixel is represented by a binary code
     • The number of bits per pixel will depend on the amount of colours avaliable

8. Sound is sampled and stored digitally

   • Sound is recorded by a microphone as an analogue system
     • Analogue Signals
       • Analogue signals are pieces of continually changing data
       • These need to be converted into digital data so that computers can read and store sound files
         • The process of converting analogue to digital is called sampling

9. Storing Sound

   • Sound is recorded by a microphone as an Analogue Signal
     • Analogue Signal
       • Analogue Signals are continually changing data
       • Analogue Systems need to be converted into digital date so computers can read and store the files
         • The process of converting Analogue to Digital is called Sampling
   • Bit Rate
     • Bit rate = Sampling Frequency x Sample Size

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