Converting Binary To Decimal

Introduction

Converting binary numbers to decimal is a fundamental process in computer science and digital systems. The binary number system, composed of 0s and 1s, is extensively used in computing and serves as the foundation for digital data representation. In this article, we will explore the concept of binary to decimal conversion, provide an understanding of the process, discuss the approach to conversion, present a step-by-step solution, and provide a code example.

Approach

To convert a binary number to decimal, we can follow the following approach:

1. Start with the given binary number.

2. Begin from the rightmost digit (units place).

3. Multiply each binary digit by the corresponding power of 2 based on its position.

4. Sum up the products obtained in step 3 to get the decimal representation.

Step-by-Step Solution

Let's illustrate the conversion process using an example:

Example

Convert the binary number 101010 to decimal.

Step 1: Start with the binary number 101010. 

Step 2: Begin from the rightmost digit (0) and assign a position value of 2^0 (units place). 

Step 3: Multiply the rightmost digit (0) by the corresponding power of 2 (2^0), resulting in 0. 

Step 4: Move to the next digit (1) and assign a position value of 2^1 (twos place). 

Step 5: Multiply the digit (1) by the corresponding power of 2 (2^1), resulting in 2. 

Step 6: Repeat steps 4 and 5 for each subsequent digit, assigning increasing powers of 2. 

Step 7: Sum up the products obtained in step 5: 0 + 2 + 0 + 8 + 0 + 32 = 42.

Therefore, the binary number 101010 is equivalent to the decimal number 42.

Code

Here's an example implementation for converting a binary number to decimal: