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Binary to Decimal Formula

Binary numbers are those which contains digits 0 and 1 in it. In Binary number system its quite natural that we convert decimal to binary and binary to decimal. They are mostly used in digital computations. The binary can be converted in to decimals easily.The Binary to decimal formula is
Binary to Decimalwhere N is decimal equivalent,
b is the digit,
q is the base value that starts from most significant digit order qn to least significant order q-1, q-2, .....

Lets see a simple illustration to know it:
Binary to Decimal Method

Related Calculators
Binary to Decimal Calculator Convert Decimal to Binary Calculator
Binary Calculator
 

Binary to Decimal Examples

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Lets see some examples based on binary to decimal conversion:

Solved Examples

Question 1: Convert 10110.11 to decimal
Solution:
 
Given Binary number is 10110.11

10110.11 = (1 $\times$ 24) + (0 $\times$ 23) + (1 $\times$ 22) + (1 $\times$ 21) + (0 $\times$ 20) + (1 $\times$ 2-1) + (1 $\times$ 2-2)
                 = (1 $\times$ 16) + (0) + (1 $\times$ 4) + (1 $\times$ 2) + (0) + $\frac{1}{2}$ + $\frac{1}{4}$
                 = 16 + 4 + 2 + 0.5 + 0.25
                 = 22.75
 

Question 2: Convert 0110101 to decimal
Solution:
 
Given Binary number is 0110101
0110101 = (0 $\times$ 26) + (1 $\times$ 25) + (1 $\times$ 24) + (0 $\times$ 23) + (1 $\times$ 22) + (0 $\times$ 21) + (0 $\times$ 20)
                 = 0 + (1 $\times$ 32) + (1 $\times$ 16) + 0 + (1 $\times$ 4) + 0 + 0         
                 = 0 + 32 + 16 + 0 + 4 + 0 + 0
                 = 52
 

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