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Binary to Decimal Converter

Easily convert the binary number to decimal number by using our converter TO-Tools.

Binary to Decimal Converter ⬇️

How to convert Binary to Decimal by manual calculation

There are two methods to convert a binary number to a decimal number system.

  1. Positional Notation Method
  2. Doubling Method

Binary to Decimal Conversion Using Positional Notation Method

In any binary number, the rightmost digit is called the ‘Least Significant Bit’ (LSB) and the left-most digit is called the ‘Most Significant Bit’ (MSB). For a binary number with ‘n’ digits, the least significant bit has a weight of 20 and the most significant bit has a weight of 2n-1.

Let us take one simple example, Consider the binary number (10101)2 

  • Step 1: List out the powers of 2 for all the digits starting from the right-most position. The first power would be 20 and as we move on it will be 21, 22, 23, 24, 25,… In the given example, there are 6 digits, therefore, starting from the right-most digit, the weight of each position from the right is 20,21,22,23,24,25.
    Binary Number : 1 0 1 0 1 0
    Power Of 2 : 25 24 23 22 21 20
  • Step 2: Now multiply each digit in the binary number starting from the right with its respective weight based on its position and make the formula and evaluate the product. As shown below.

    (101010)=  (1⋅25) + (0⋅24) + (1⋅23) + (0⋅22) + (1⋅21) + (0⋅20)  =  (42)10

  • Step 3: Now, We express the binary number as a decimal number:

    (101010)2 = (42)10

Binary to Decimal Conversion Using Doubling Method

Let us use the same example for converting the binary number (101010)2 to decimal.

  • Step 1: Write the binary number and start from the left-most digit. Double the previous number and add the current digit. Since we are starting from the left-most digit and there is no previous digit to the left-most digit, we consider the double of the previous digit as 0. For example in (101010)2, the left-most digit is ‘1’. The double of the previous number is 0. Therefore, we get [(0 × 2) + 1] which is 1.
  • Step 2: Continue the same process for the next digit also. The second digit from the left is 0. Now, double the previous digit and add it with the current digit. Therefore, we get, [(1 × 2) + 0], which is 2.
    Binary Number 0 x 2 0
    1 0 1 0 1 0 (0 x 2) + 1 1
    1 0 1 0 1 0 (1 x 2) + 0 2
    1 0 1 0 1 0 (2 x 2) + 1 5
    1 0 1 0 1 0 (5 x 2) + 0 10
    1 0 1 0 1 0 (10 x 2) + 1 21
    1 0 1 0 1 0 (21 x 2) + 0 42
    (Decimal Value)
  • Step 3: Continue the same step in sequence for all the digits. The sum that is achieved in the last step is the actual decimal value. As shown in the table. Therefore, the result of converting the binary number to a decimal using the doubling method is
    (101010)2 = (42)10.

Binary to decimal conversion table

Binary Number Decimal Number Hex Number
0 0 0
1 1 1
10 2 2
11 3 3
100 4 4
101 5 5
110 6 6
111 7 7
1000 8 8
1001 9 9
1010 10 A
1011 11 B
1100 12 C
1101 13 D
1110 14 E
1111 15 F
10000 16 10
10001 17 11
10010 18 12
10011 19 13
10100 20 14
10101 21 15
10110 22 16
10111 23 17
11000 24 18
11001 25 19
11010 26 1A
11011 27 1B
11100 28 1C
11101 29 1D
11110 30 1E
11111 31 1F
100000 32 20
1000000 64 40
10000000 128 80
100000000 256 100

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