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Decimal and binary are two different number systems commonly used in various fields, such as computer science and mathematics. Decimal, also known as base-10, is the numerical system most familiar to us, where numbers are represented using ten different symbols (0-9). On the other hand, binary, often referred to as base-2, is a numerical system that uses only two symbols (0 and 1). Converting a decimal number to its binary equivalent can be a useful skill when working with binary codes or understanding how computers process information. In this guide, we will explore the step-by-step process of converting a decimal number to binary, providing techniques and examples to help you understand and master this conversion method. Whether you are a computer science student, a programmer, or simply interested in expanding your knowledge, learning how to convert from decimal to binary is a valuable skill that can enhance your understanding of number systems and their applications. So, let’s dive into the world of binary and unravel the process of converting decimal numbers to their binary counterparts.
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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] X Research 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
- 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.
- 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.
- 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
- 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] X Research 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 relatively simple process that involves dividing the decimal number by 2 repeatedly until the quotient becomes zero. The remainders obtained at each step are then written in reverse order to obtain the binary representation of the decimal number. This method allows us to represent decimal numbers in a binary format, which is essential in various computational tasks, such as computer programming and digital data storage. By understanding the steps involved in this conversion process, individuals can effectively convert decimal numbers to binary and make use of binary representations in various applications.
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