Computer Science (0984) 2023 - 1 Data Representation 1-1

1-1 Number Systems

1-1-1 Understand how and why computers use binary to represent all forms of data

• Any form of data needs to be converted to binary to be processed by computer.
• Data is processed using logic gates and stored in registers.

1-1-2 Understand the denary, binary and hexadecimal number systems

• Denary is a base 10 system 
  10 000   1 000   100    10       1
  (10⁴)       (10³)  (10²)  (10¹)  (10⁰)
• Binary is a base 2 system 
  128     64     32     16     8     4      2      1
  (2⁷)    (2⁶)   (2⁵)   (2⁴)  (2³) (2²)  (2¹)  (2⁰)
  Typical binary numer looks like 1110 0110
• Hexadecimal is a base 16 system
  Uses number 0 to 9 and letters A to F where A=10, B=11, C=12, D=13, E=14 and F=15

1-2-3 Convert

• Binary to Denary
  
  • Place binary number in base 2 colummns
  • Then add base 2 numbers where a 1 appears

    128     64     32     16     8     4      2      1   (base 2 numbers)
       1       0       1       0      1     0      0      0   (binary number 1010 1000)
    128 + 32 + 8 = 168                                    (add base 2 numbers)

• Denary to Binary
  
  • Create base 2 columns
  • Starting at the left, indicate how many times the base 2 number can go into your denary number
  • Example: 84
    128 …