Data representation

Data representation

1. Units

   • A bit is a single binary digit that can have the values of 0 or 1
   • A Byte is a group of eight bits, the maximum decimal number it can store is 255
   • A Nibble is a group of four bits
   • A Kilobyte is 1024 bytes
     • A MegaByte is 1024 Kilobytes
       • A Gigabyte is 1024 Kilobytes
         • A Terabyte is 1024 Gigabytes
   • Binary code is based on a number system that uses two digits - 0 and 1
     • All computer systems store data and insturction using binary code because digital computers can only process binary
       • This means all data inputted into the system must be converted to binary

2. Number

   • The denary number system is based on the decimal system and uses the digits 0 to 9
     • When adding binary numbers be careful of overflow, this is where two or more binary numbers are added but the result is too large to fit into the bits allocated
   • To convert Denary into Binary you must create a table with binary place values
     • Start by finding the largest place value equal to that number and then subtract that place value from the number
       • Then find the next highest place value equal to that number
         • You must continue this until you have filled in the table
     • When converting Binary to Denary once again make an 8-bit table table, but this time add all the numbers above each 1 together
   • The Hexadecimal number system is based on 16 states - digits 0 to 9 and letters A to F
     • When converting between hexadecimal, denary and binary you need to reference and learn the tables so you know what is equivalent to whatt
       • For example 1111 in Binary is equivalent to 15 in Denary and F in Hexadecimal
     • Hexadecimal is often used as it is easy to convert, 4 bits per hex, easier to remember - this means less errors are made

3. Characters

   • ASCII is a seven-bit character set which offers 128 differemt characters
   • Unicode is a 16-bit character set which offers 65.536 different characters
   • Character sets are a list of all the character accessible to a computer system
   • The number of bits per character effects the storage space needed when using that character set, for example ASCII uses one byte per character - Unicode uses two
   • The number of characters that can be represented effects what system that character set can be used for
     • Unicode can support any language in the world and has enough characters for controlling peripheral devices
     • ASCII with a much smaller character set can only support certain languages

4. Images

   • Pixels are the smallest elements in a digital image
     • Images consist of many pixels that overall make an image
       • Image's however must be stored in a binary format so they can be used on computers
         • In basic black and white photos 1 = black and 0 = white
         • However, colour can be shown in images by using more bits per pixel
           • For example, 16 bites per pixel can allow a range of 65,636 colours to be shown rather than two at 1 bit per pixel
   • Metadata is needed in an image file as it gives details of image height, width and colour depth
     • Colour depth is the number of bits used for each pixel, where 1 bit is black and white and 8 bits gives 256 colours
     • Height and width are needed to decide the amount of pixels width and height an image should be
     • Resolution effects the size of an image file because the higher the resolution the more pixels needed to make that image up which makes the size of the file larger

5. Sound

   • Sound can be stored as binary files and output to a computer using a microphone
     • An ADC is used to create a digital sound signal
   • When sound waves are input into a computer they are converted digitally in a file composed of a set of binary numbers
   • Sampling rate is the number of samples taken per second from the analogue data inputted to create a digital signal
     • When this rate is high the sound quality is better but the file size larger
     • When this rate is low the sound quality is lower and the file size lower

6. Instructions

   • Instructions are coded as bit patterns because the CPU can easily fetch the instruction and decode it, update the program counter, process and decode the program instruction which consists of an operator and the operand
     • This process is then repeated
   • The Operator is the first four bits of a 8-bit binary and the operand is the last four bits of that 8-bit binary