1.1 Number Systems

Any form of data needs to be converted to binary to be processed by a computer.

Denary+Binary+Hexadecimals

  • Binary system : Base 2. Represented using 0 and 1
  • Denary system: Base 10. Represented with numbers from 0-9
  • Hexadecimal: Base 16. Represented with symbols 0-9 and letters A-F

Explain why a computer can only process binary data

  • Computer consist of transistors/logic circuits
  • ..that can only store process data in two states(on/off)

What is an overflow error? When does it occur?

  • A computer has a predefined limit that it can represent (eg. 8bits)
  • ..Overflow occurs when a value outside this limit should be returned
  • Can occur when two binary numbers are added together
  • …the result is cannot be represented in the current register.
  • eg. 255+10 in binary cannot be represented in the current size of the register.
  • Solution: use a 16 bit/2byte register

Uses of hexadecimals:

  • Error codes. Eg#404
  • Representation of colours on a website. Eg FFFFFF
  • Memory dumps: output the contents of memory on screen

MAC address:

  • made up of 48 bits
  • shown as 6 groups of two hexadecimal digits
  • First half represents Manufacturer
  • Second half represents Serial number
  • Uniquely identifies a device on the network
  • eg. 11:11:11:11:11:11
  • MEDIA ACCESS CONTROL (only use if not referred by the question!)

Why do programmers/developers use hexadecimal (vs binary)

  • Shorter in length compared to binary eg. Hex FFF1 🡪binary 1111111111110001
  • …Making them easier to read/understand
  • …Easier to debug