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We communicate using words and characters. We are familiar with numbers, characters, and words. However, this type of data is incompatible with computers. Computers can only comprehend numbers. As a result, when we enter information, it is converted into an electronic pulse. ASCII converts the code from each pulse into a numeric format. It assigns a numerical value (number) to each number, character, and symbol. So, to understand computer language, one must be familiar with number systems. Here we explore more about the number system in computers, types of the number system in computers, and conversion of the number system in computers.<\/p>\n
A number system is a method of writing numbers that is a mathematical way of representing the numbers of a given set by mathematically using numbers or symbols. A number system is defined as a writing system for denoting numbers logically using digits or symbols. The numeral system represents a useful set of numbers, reflects a number’s arithmetic and algebraic structure, and offers standard representation. All numbers can be formed using the digits 0 to 9. Anyone can generate an infinite number using these digits. For instance, 156,3907, 3456, 1298, 784859, and so on.<\/p>\n
Number system in computer The most commonly used number system is the binary system, also known as the base-2 number system. The binary system uses only two digits, 0 and 1, to represent all numbers and data.<\/p>\n
Binary numbers are used extensively in digital electronics and computing because it is easy to represent them using switches, where 0 represents "off" and 1 represents "on." This makes it possible to store and manipulate data electronically using digital circuits.<\/p>\n
These systems are often used for representing and manipulating large binary numbers or for expressing memory addresses in a compact and easy-to-read format. Computer programs and programming languages use number system concepts to perform arithmetic operations, store data, and communicate with hardware devices.<\/p>\n
There are mainly four types of the number system in computer<\/p>\n
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Hexadecimal Number System:<\/strong> The hexadecimal number system uses 16 digits, including 0 through 9 and A through F, to represent numbers. It is often used in computer programming and digital electronics.<\/p>\n Each of these number systems has its advantages and disadvantages, and each is used in different applications. For example, the binary number system is used to represent and manipulate data in computer hardware, while the decimal number system is used for everyday calculations. The octal and hexadecimal systems are commonly used in computer programming and digital electronics because they are more compact and easier to read than binary.<\/p>\n Converting between number system in computer science is an important skill, especially when working with binary, octal, and hexadecimal numbers. Here are the basic steps to convert a number from one number system to another:<\/p>\n Understand the values of each digit in the current number system: Before you can convert a number, you need to understand how the current number system works. For example, in the binary system, each digit represents a power of two, starting with 20 on the right side.<\/p>\n Convert the number to decimal: To convert a number from any base to decimal, you need to multiply each digit by its corresponding power of the base and add up the results. For example, to convert the binary number 1011 to decimal, you would calculate (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20) = 8 + 0 + 2 + 1 = 11.<\/p>\n Check your answer: To verify your answer, you can convert the number back to the original base and make sure it matches the original number.<\/p>\n Example:<\/strong> Convert the decimal number 158 to binary, octal, and hexadecimal. Binary Conversion:<\/strong> 158 \/ 2 = 79 remainder 0 Therefore, the binary equivalent of 158 is 10011110.<\/p>\n<\/li>\n Octal Conversion:<\/strong> 158 \/ 8 = 19 remainder 6 Therefore, the octal equivalent of 158 is 236.<\/p>\n<\/li>\n Hexadecimal Conversion:<\/strong> 158 \/ 16 = 9 remainder 14 (E) Therefore, the hexadecimal equivalent of 158 is 9E.<\/p>\n Output<\/strong><\/p>\n Code Implementation<\/strong><\/p>\n\t\t\t\t\t\t![\"\"](\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1681123071641-1-02%20%2834%29.png\")
<\/p>\n<\/li>\n<\/ul>\nConversion of the Number System in the Computer<\/h2>\n
\nBelow is the conversion one by one:<\/p>\n\n
\nTo convert a decimal number to binary, we divide the decimal number by 2 repeatedly and write the remainder in reverse order.<\/p>\n
\n79 \/ 2 = 39 remainder 1
\n39 \/ 2 = 19 remainder 1
\n19 \/ 2 = 9 remainder 1
\n9 \/ 2 = 4 remainder 1
\n4 \/ 2 = 2 remainder 0
\n2 \/ 2 = 1 remainder 0
\n1 \/ 2 = 0 remainder 1<\/p>\n
\nTo convert a decimal number to an octal, we divide the decimal number by 8 repeatedly and write the remainder in reverse order.<\/p>\n
\n19 \/ 8 = 2 remainder 3
\n2 \/ 8 = 0 remainder 2<\/p>\n
\nTo convert a decimal number to hexadecimal, we divide the decimal number by 16 repeatedly and write the remainder in reverse order. For remainders greater than 9, we use letters A-F.<\/p>\n
\n9 \/ 16 = 0 remainder 9<\/p>\nDecimal: 158\nBinary: 10011110\nOctal: 236\nHexadecimal: 9E<\/code><\/pre>\n<\/li>\n<\/ul>\n