2.1.9 – 2.1.11 – Binary representation

2.1.9 Define the terms: bit, byte, binary, denary/decimal, hexadecimal

Numbering Systems

  • Denary (or normal numbers as we know them are BASE 10 )
    • This is because we use 0-9
  • Binary is BASE 2
    • This is because it uses a 1 and a 0
  • Hexadecimal is BASE 16
    • This is because Hexadecimal ranges from 0-9 then A=10 B=11 C=12 D=13 E=14 F=15

Bits & Bytes

Highest Numbers and colours

  • 8 bit maximum would be 11111111 = 255 so 255 is the highest number
  • BUT when we talk about how many different colours, 00000000 also counts as a colour so the answer is 256
  • 16 bit gives us 65536 different colours

Sizes

2.1.10 – Outline the way in which data is represented in the computer

Hexadecimal to Denary

Denary to Hexadecimal

Hexadecimal values in colours

Unicode & ASCII

ASCII and Unicode are two character encodings.

Basically, they are standards on how to represent difference characters in binary so that they can be written, stored, transmitted, and read in digital media.

The main difference between the two is in the way they encode the character and the number of bits that they use for each.

ASCII

  • ASCII uses 8 bits to encode characters. It was 7 bit which allowed different characters numbered  0-127
  • ASCII uses the 8th bit to leave room for 128 additional characters, which are used to represent a host of foreign language and other symbols.
  • If none of the additional character combinations is used (128-255), the first bit of the byte is 0

Unicode

  • Unicode uses a variable bit encoding program where you can choose between 8, 16, and 32 bit encodings (giving you 2,147,483,647 different types).
  • Using more bits lets you use more characters at the expense of larger files while fewer bits give you a limited choice but you save a lot of space.
  • Using fewer bits (i.e. UTF-8) would probably be best if you are encoding a large document in English.