Hexadecimal to Denary

Convert hexadecimal to denary:

Hexadecimal is base 16, this means there are 16 digits: 0-9 and A-F. You can see the table adjacent what each hexadecimal digit is equivalent to.

The 16 times table can be useful: 

          1x   2x   3x   4x   5x   6x   7x   8x   9x   10x
          16   32   48   64   80   96   112  128  144  160
Example conversion

Convert the hexadecimal number 5D to denary:


          16    1                      D is 13
          5     D          (5 * 16) + (D * 1) 
                           (5 * 16) + (13 * 1) = 93
        
          Hex    Den    Bin
          0      0      0000
          1      1      0001
          2      2      0010
          3      3      0011
          4      4      0100
          5      5      0101
          6      6      0110
          7      7      0111
          8      8      1000
          9      9      1001
          A      10     1010
          B      11     1011
          C      12     1100
          D      13     1101
          E      14     1110
          F      15     1111

The hexadecimal number system uses column headings of 1 and 16, multiplying by 16 each time as the number system is base 16. You only need to know 2 digit hexadecimal numbers for GCSE.

Overview

To convert a hexadecimal number into denary, multiply each digit by its place value and add them together.

As hexadecimal is base 16, that means there are 16 different digits and we need to use more than just 0-9 from denary. Therefore A-F are introduced. As you can see in the table below, each hexadecimal digit is equivalent to a binary nibble.

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

Convert A3 to denary:

  • Write the hexadecimal number underneath the column headings: 
    
          16    1
          A     3
  • Convert any letters to their denary equivalents: A = 10 
    
          16    1
          10    3
  • Multiply each digit by its place value: (10 × 16) + (3 × 1)
  • Calculate: 160 + 3 = 163
  • Therefore A316 = 16310

References: