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Converting from decimal to binary is an essential skill in computer science and mathematics. Binary numeral system, also known as base-2, uses only two digits: 0 and 1. In contrast, the decimal numeral system, based on the number ten, uses ten different digits from 0 to 9. Understanding how to convert decimal numbers to binary is crucial for tasks such as coding, data representation, and understanding the inner workings of computer systems. By learning the step-by-step process of converting from decimal to binary, individuals can easily manipulate and interpret binary data efficiently. This guide will provide a clear and concise explanation of the steps involved, enabling anyone to confidently convert decimal numbers to binary and unleash their understanding of this fundamental concept.
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The decimal system (base ten) has ten values (0,1,2,3,4,5,6,7,8, or 9) for each value. In contrast, the binary system (base two) has two representations of 0 and 1 for each value. [1] XResearch Source Since binary is an intrinsic language used in electronic computers, computer programmers should understand how to convert from decimal to binary. Follow these simple steps to see how to convert.
Steps
Short division by Two with Remainder
![Image titled Convert from Decimal to Binary Step 1](https://www.wikihow.com/images_en/thumb/b/b5/Convert-from-Decimal-to-Binary-Step-1-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-1-Version-4.jpg)
- This method is easier to understand when described on paper, and much easier for beginners, because it relies only on division by two.
- To avoid confusion before and after conversion, write the number of the base system you are working on below each number. In this case, the decimal number will have a subscript of 10 and the binary equivalent will have a subscript of 2.
![Image titled Convert from Decimal to Binary Step 2](https://www.wikihow.com/images_en/thumb/c/c2/Convert-from-Decimal-to-Binary-Step-2-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-2-Version-4.jpg)
- Since we divide by 2, when the number being divided is even the binary remainder will be 0, and when the number being divided is odd the binary remainder will be 1.
![Image titled Convert from Decimal to Binary Step 3](https://www.wikihow.com/images_en/thumb/8/85/Convert-from-Decimal-to-Binary-Step-3-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-3-Version-4.jpg)
![Image titled Convert from Decimal to Binary Step 4](https://www.wikihow.com/images_en/thumb/b/b2/Convert-from-Decimal-to-Binary-Step-4-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-4-Version-4.jpg)
- This method can be adapted to convert from decimal to ‘any’ system. The divisor is 2 because the system you want to convert is 2 (binary). If the conversion system is another system, replace the divisor by 2 in the calculation with the system you want to convert. For example, if the system you want to convert is a 9, replace the divisor 2 with the number 9. The final result will be according to the system you want to convert.
Decreasing Powers and Subtraction
![Image titled Convert from Decimal to Binary Step 5](https://www.wikihow.com/images_en/thumb/1/1a/Convert-from-Decimal-to-Binary-Step-5-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-5-Version-4.jpg)
![Image titled Convert from Decimal to Binary Step 6](https://www.wikihow.com/images_en/thumb/c/c0/Convert-from-Decimal-to-Binary-Step-6-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-6-Version-4.jpg)
![Image titled Convert from Decimal to Binary Step 7](https://www.wikihow.com/images_en/thumb/8/8f/Convert-from-Decimal-to-Binary-Step-7-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-7-Version-4.jpg)
![Image titled Convert from Decimal to Binary Step 8](https://www.wikihow.com/images_en/thumb/2/22/Convert-from-Decimal-to-Binary-Step-8-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-8-Version-4.jpg)
![Image titled Convert from Decimal to Binary Step 9](https://www.wikihow.com/images_en/thumb/4/45/Convert-from-Decimal-to-Binary-Step-9-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-9-Version-4.jpg)
![Image titled Convert from Decimal to Binary Step 10](https://www.wikihow.com/images_en/thumb/d/d7/Convert-from-Decimal-to-Binary-Step-10-Version-4.jpg/v4-460px-Convert-from-Decimal-to-Binary-Step-10-Version-4.jpg)
- Repeating this method will help memorize powers of 2, allowing you to skip step 1.
Advice
- The computer installed in your operating system can do this conversion for you, but as a programmer you should have a clear understanding of how the conversion works. You can view your computer’s conversion options by opening the “View” section of the toolbar and selecting “Programmer”.
- Converting backwards, from binary to decimal, is usually easier to learn first.
- Practice. Try converting decimals 178 10 , 63 10 , and 8 10 . The corresponding binary numbers are 10110010 2 , 111111 2 , and 1000 2 . Try converting 209 10 , 25 10 , and 241 10 to the binary numbers 11010001 2 , 11001 2 , and 11110001 2 respectively.
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 94 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 207,215 times.
The decimal system (base ten) has ten values (0,1,2,3,4,5,6,7,8, or 9) for each value. In contrast, the binary system (base two) has two representations of 0 and 1 for each value. [1] XResearch Source Since binary is an intrinsic language used in electronic computers, computer programmers should understand how to convert from decimal to binary. Follow these simple steps to see how to convert.
In conclusion, converting from decimal to binary is a simple and straightforward process that can be accomplished by following a few key steps. By understanding the significance of the place values in the binary number system and using basic division and remainder operations, one can easily convert any decimal number to its binary representation. It is important to remember that binary numbers only consist of 0s and 1s, representing the absence or presence of a specific power of 2. Although this conversion process may seem daunting at first, with practice and familiarity, one can quickly master the art of converting from decimal to binary. This skill is particularly useful in computer science and programming, as binary numbers are the fundamental building blocks of digital information and data storage. Therefore, grasping this conversion technique will undoubtedly enhance one’s understanding of the binary number system and foster a deeper comprehension of the inner workings of computers and digital systems.
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