February 28, 2025

Conversion of Numbers

 

The following offers some rules for conversion of numbers between differing number systems. You may find other approaches that are more suitable (and understandable) e.g. the tabular layout outlined on the previous three pages.

Decimal Binary Hex Octal
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 7 7
8 1000 8 10
9 1001 9 11
10 1010 A 12
11 1011 B 13
12 1100 C 14
13 1101 D 15
14 1110 E 16
15 1111 F 17

 

Examples

  1. Binary to Octal Conversion : Binary Number 1001001011110101
    Split into groups of 3 binary digits (bits) starting from the right.
    1 001 001 011 110 101 Binary
    1   1   1    3     6      5 Octal
  2. Binary to Hexadecimal Conversion : Binary Number 1001001011110101
    Split into groups of 4 bits starting from the right.
    1001 0010 1111 0101 Binary
       9      2      F      5   Hexadecimal
  3. Decimal to Binary:
    Example:
    Convert 46(base 10) to binary.
    Divide the number successively by 2 and note the remainders (0 or 1). Write down these remainders, starting from the right and working left.
    46 / 2 rem 0                0
    23 / 2 rem 1               10
    11 / 2 rem 1              110
      5 / 2 rem 1            1110
      2 / 2 rem 0           01110
      1 / 2 rem 1         101110
      0
    Binary                0101110

Next page » Binary addition

Previous page « Hexadecimal Number System

 

 

 

 

 

 

 

 

 

 

 

 

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