Binary to Decimal Conversion with Example

This page was written and published in order to provide an explanation of the process that enables us to convert binary numbers to the corresponding decimal values. However, before we get started, it is important that you have an understanding of the following numbers: binary numbers and decimal numbers.

  • Binary numbers: Binary numbers are ones that can be created using only the digits 0 and 1, as they are the only two digits available. To put it another way, we can say that a number that is made up of simply the digits 0 and 1 is what is known as a binary number. Examples include 11101, 00111101, and 11010, amongst others.
    One additional thing to keep in mind about binary numbers is that binary numbers have a base of 2, which means that a binary number has a total of two digits, which are the digits 0 and 1.
  • Decimal numbers: Decimal numbers, on the other hand, are those that have any 10 digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. 124, 4302, and 2039 are a few examples among many others. To put it another way, decimal numbers are ones that can contain any integer value between 0 and 9, inclusive.
    One final aspect to note regarding decimal numbers is that 10 is their base.

No, I think these details are enough; let's move on to the main topic, which is the conversion of binary to decimal.

Binary to decimal conversion formula

In order to convert any binary number, such as 101110, to a decimal number, we need to follow the rules that are displayed in the box that can be seen 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 conversion steps

The following is a rundown of the procedures involved in converting binary to decimal, as outlined in the box located above:

  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 a binary number, which should be written below 20 or 1.
  4. Finally, in the fourth line, below each and every 1, write down the values of the second step in the corresponding columns of 1's.
  5. Now sum up all the values from the fourth step.
  6. The sum will be the equivalent decimal value of the given binary number.

Binary to decimal conversion example

The coefficients of a binary number are multiplied by the power of 2 to convert any number presented in binary form or using a binary number system into a decimal number system. Take this as an illustration: 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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