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Binary and decimal number systems are two widely used and fundamentally different ways of representing numbers. While decimal is the system we typically use in our daily lives, binary is commonly used in computer science and digital technology. Understanding how to convert from binary to decimal is a fundamental skill for anyone working with computers or studying computer science. This conversion process allows us to interpret binary values as decimal numbers, enabling us to perform calculations and make sense of the data stored in binary form. In this guide, we will explore the step-by-step process of converting from binary to decimal, providing clear explanations and practical examples along the way. By the end, you will have a solid understanding of how to convert binary numbers to their decimal equivalents, enabling you to work with and manipulate binary data effectively.
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 120 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 339,533 times.
The binary system is the internal language of electronic computers. As a real programmer, you need to know how to convert from binary to decimal . In this article, wikiHow will show you how.
Steps
Use position notation
![Image titled Convert from Binary to Decimal Step 1](https://www.wikihow.com/images_en/thumb/8/8f/Convert-from-Binary-to-Decimal-Step-1-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-1-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 2](https://www.wikihow.com/images_en/thumb/f/f0/Convert-from-Binary-to-Decimal-Step-2-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-2-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 3](https://www.wikihow.com/images_en/thumb/f/f9/Convert-from-Binary-to-Decimal-Step-3-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-3-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 4](https://www.wikihow.com/images_en/thumb/e/e2/Convert-from-Binary-to-Decimal-Step-4-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-4-Version-5.jpg)
- Since “1” corresponds to “1”, our final value will be “1”. “2” corresponds to “1” so the final value will be “2”. “4” corresponds to “0” so the final value will be “0”. “8” corresponds to “1” so the final value is “8” and “16” corresponds to “1” so we have “16”. “32” corresponds to “0” and returns “0”. “64” corresponds to “0” so the final value is “0” while “128” corresponds to “1” so we have 128.
![Image titled Convert from Binary to Decimal Step 5](https://www.wikihow.com/images_en/thumb/8/8b/Convert-from-Binary-to-Decimal-Step-5-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-5-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 6](https://www.wikihow.com/images_en/thumb/3/30/Convert-from-Binary-to-Decimal-Step-6-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-6-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 7](https://www.wikihow.com/images_en/thumb/e/e2/Convert-from-Binary-to-Decimal-Step-7-Version-4.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-7-Version-4.jpg)
- “1” to the left of the comma is equivalent to 2 0 , or 1. 1 to the right of the comma is equivalent to 2 -1 , or ,5. Adding 1 to ,5 gives 1.5, which is 1.1 2 when expressed in decimal notation.
Use the double method
![Image titled Convert from Binary to Decimal Step 8](https://www.wikihow.com/images_en/thumb/0/01/Convert-from-Binary-to-Decimal-Step-8-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-8-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 9](https://www.wikihow.com/images_en/thumb/5/52/Convert-from-Binary-to-Decimal-Step-9-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-9-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 10](https://www.wikihow.com/images_en/thumb/c/cd/Convert-from-Binary-to-Decimal-Step-10-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-10-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 11](https://www.wikihow.com/images_en/thumb/3/3e/Convert-from-Binary-to-Decimal-Step-11-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-11-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 12](https://www.wikihow.com/images_en/thumb/2/29/Convert-from-Binary-to-Decimal-Step-12-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-12-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 13](https://www.wikihow.com/images_en/thumb/0/03/Convert-from-Binary-to-Decimal-Step-13-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-13-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 14](https://www.wikihow.com/images_en/thumb/5/5f/Convert-from-Binary-to-Decimal-Step-14-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-14-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 15](https://www.wikihow.com/images_en/thumb/4/4a/Convert-from-Binary-to-Decimal-Step-15-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-15-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 16](https://www.wikihow.com/images_en/thumb/5/5b/Convert-from-Binary-to-Decimal-Step-16-Version-5.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-16-Version-5.jpg)
![Image titled Convert from Binary to Decimal Step 17](https://www.wikihow.com/images_en/thumb/2/2b/Convert-from-Binary-to-Decimal-Step-17-Version-3.jpg/v4-460px-Convert-from-Binary-to-Decimal-Step-17-Version-3.jpg)
Advice
- Practice. Try swapping the binary numbers 11010001 2 , 11001 2 , and 11110001 2 . They correspond to 209 10 , 25 10 , and 241 10 , respectively .
- A PC pre-installed with Microsoft Windows can do the conversion for you, but as a programmer you should understand how this conversion works. You can display the conversion options on your computer by opening the “View” menu and choosing “Scientific” or “Programmer”. On Linux, you can use a personal computer.
- Note: this article is ONLY about the calculation and not about the ASCII encoding.
Warning
- This article uses unsigned binary numbers instead of signed numbers, static floating point real numbers, or floating point real numbers.
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 120 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 339,533 times.
The binary system is the internal language of electronic computers. As a real programmer, you need to know how to convert from binary to decimal . In this article, wikiHow will show you how.
In conclusion, converting from binary to decimal may seem intimidating at first, but with the proper understanding of the concept and a step-by-step approach, it becomes a straightforward process. By summarizing the steps discussed in this guide, converting from binary to decimal involves identifying the place values of each binary digit, multiplying each digit by its corresponding place value, and then summing up these products to obtain the decimal equivalent. The key to success is to practice and become familiar with the conversion process, as it will strengthen one’s numerical skills and problem-solving abilities. By mastering this skill, individuals can efficiently work with binary numbers and understand their decimal equivalents, which can be valuable in various fields such as computer science, programming, and digital electronics. With perseverance and regular practice, anyone can become proficient in converting from binary to decimal, unlocking a deeper understanding of number systems and their applications in the modern world.
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