How to convert binary to decimal

Converting binary numbers to decimal is an essential skill in computer science and mathematics. This blog will explore two primary methods for performing this conversion: the Positional Notation Method and the Doubling Method.
Understanding Binary and Decimal Systems
Before diving into the conversion methods, it's crucial to understand the difference between binary and decimal systems:
Binary System: A base-2 numeral system that uses only two digits, 0 and 1.
Decimal System: A base-10 numeral system that uses ten digits, from 0 to 9.
Conversion Methods

1. Positional Notation Method This method involves multiplying each binary digit by 2 2 raised to the power of its position, starting from the rightmost digit (which is position 0). Steps: Write down the binary number. Starting from the rightmost digit, assign powers of 2 2 to each digit. Multiply each binary digit by its corresponding power of 2 2. Sum all the results to get the decimal equivalent. Example: Convert 101 1 2 1011 2 ​ to decimal. 1 × 2 3 = 8 1×2 3 =8 0 × 2 2 = 0 0×2 2 =0 1 × 2 1 = 2 1×2 1 =2 1 × 2 0 = 1 1×2 0 =1 Adding these together gives: 8 + 0 + 2 + 1 = 11 8+0+2+1=11 Thus, 101 1 2 = 1 1 10 1011 2 ​ =11 10 ​ .
2. Doubling Method This method involves starting from the leftmost digit and doubling the previous total while adding the current digit. Steps: Write down the binary number. Start with a total of zero. Move from left to right, doubling the total and adding the current binary digit at each step. Example: Convert 110 1 2 1101 2 ​ to decimal. Start with an initial total of 0 0. For the first digit (1): ( 0 × 2 ) + 1 = 1 (0×2)+1=1 For the second digit (1): ( 1 × 2 ) + 1 = 3 (1×2)+1=3 For the third digit (0): ( 3 × 2 ) + 0 = 6 (3×2)+0=6 For the fourth digit (1): ( 6 × 2 ) + 1 = 13 (6×2)+1=13 Thus, 110 1 2 = 1 3 10 1101 2 ​ =13 10 ​ . Conclusion Both methods are effective for converting binary numbers to decimal. The Positional Notation Method is more systematic and straightforward for those who prefer mathematical formulas, while the Doubling Method can be quicker for mental calculations or programming applications. With practice, anyone can master these techniques and enhance their understanding of number systems in computing and mathematics.