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.
    • Only has 2 values
    • Represented using 0 and 1
  • Denary system:
    • Base 10.
    • Has 10 values
    • Represented with numbers from 0-9
  • Hexadecimal:
    • Base 16.
    • Has 16 values
    • 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)

Note: similar question could be explain why data needs to be converted to binary

Uses of hexadecimals:

  • Error codes. Eg#404
  • HTML colour codes. Eg FFFFFF
  • URL
  • Memory Dump
  • IP addresses
  • Assembly language
  • ASCII/Unicode

Why do Developers prefer to use Hexadecimals?

  • Easier/quicker to understand/read/write
  • Easier/quicker to debug
  • Less likely to make a mistake
  • Shorter representation//Takes up less screen space

Note: Think about the hexadecimal error code 404, the binary equivalent is: 010000000100. Which is easier to memorise?

Describe a similarity between Binary and Hexadecimal?

  • They are both number systems

Describe a difference between Binary and Hexadecimal?

  • Binary is base 2 whereas hexadecimal is base 16
  • Binary only uses numbers whereas hexadecimal also uses letters//Binary only uses 0 and 1 whereas hexadecimal uses 0 to 9 and A to F

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!)

What is an overflow error?

  • A computer has a predefined limit that it can represent (eg. 8bits)
  • ..Overflow occurs when a value outside this limit should be returned

When does it overflow occur?

  • 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

What is an overflow error?

  • A computer has a predefined limit that it can represent (eg. 8bits)
  • ..Overflow occurs when a value outside this limit should be returned

When does it overflow occur?

  • 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

What Effect does a logical shift have on a binary number

Example1: 2 Left logical shifts on the binary number: 00010011

Result: 01001100

  • The number has been multiplied by 2 to the power of 2

Example 2: 2 Left logical shifts on the binary number: 11010011

Result: 01001100

  • Most significant bits are lost. The answer is incorrect

Note: before you answer these questions look at what is happening to your binary register. if a left most bit is lost use example 2 answer otherwise example 1.

Left shifts= multiplication by 2^number of shifts

Right shifts =Division by 2^number of shifts