Binary to Denary

Convert binary to denary:

Reminder of column headings / place values for the binary number system: 128  64  32  16  8  4  2  1

Convert the binary number 01010011 to denary:


      128   64    32    16    8    4    2    1
       0     1     0     1    0    0    1    1               64 + 16 + 2 + 1 = 83

The binary number system uses column headings of 1, 2, 4, 8, 16, 32, 64, 128..., multiplying by 2 each time as the number system is base 2.

Whereas the denary number system, what we use normally, uses column headings of 1, 10, 100, 1000, 10000..., multiplying by 10 each time as the number system is base 10.

Example

To convert a binary number into denary, add up the values of the columns that contain a 1.

Place values / column headings = 128 64 32 16 8 4 2 1

Convert 00101101 to denary:

  • Write the binary number underneath the column headings: 
    
          128   64    32    16    8    4    2    1
            0    0     1     0    1    1    0    1
  • Identify which columns contain a 1: columns 32, 8, 4, and 1
  • Add up these values: 32 + 8 + 4 + 1 = 45
  • Therefore 001011012 = 4510

References: