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Binary to Decimal Conversion



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In this tutorial, you will learn step by step method used for the conversion of binary to decimal.

Binary & Decimal Number

Binary number has its base as 2. That means it has total of 2 digits that are 0 and 1. Whereas decimal number has its base as 10. That means it has total of 10 digits, that are 0, 1, 2, ..., 8, 9.

Binary to Decimal Formula

To convert any binary number say 101110 to decimal number, then we have to follow the rules as shown in the box given below:

2n.........25  24  23  22  21  20
           32  16 8   4   2   1
		  
           1   0  1   1   1   0 (binary number)
           32     8   4   2     (write value below 1 only)
=32+8+4+2                       (sum up all the values)
=46

Therefore (101110)2 = (46)10

Binary to Decimal Steps

Here are the steps that are used to convert binary to decimal as shown in above box:

  1. In first line, write 2n.........25 24 23 22 21 20
  2. In second line, write the values of .........25 24 23 22 21 20 that will be ......... 32 16 8 4 2 1
  3. And in third line, write the given binary number from right side. That is the last digit of binary number should be written below 20 or 1
  4. Finally in fourth line, below each and every 1, write down the values of second step in corresponding columns of 1's
  5. Now sum up all the values of fourth step
  6. The summation will be the equivalent decimal value of given binary number

Binary to Decimal Example

To convert any number given in binary form or binary number system into a decimal number system, then coefficient of binary number are multiplied by the power of 2. Let’s take an example.

Convert (110110)2 in binary form.

(110110)2 = ( ? )10
= 1*25 + 1*24 + 0*23 + 1*22 + 1*21 + 0*20
= 32 + 16 + 0 + 4 + 2
= ( 54 )10

Therefore, 110110 in binary will be equal to 54 in decimal.

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