1.What is a number system in computer programming?
2. what is binary, octal, hexa, DEC and how to convert them to one another?
thanky you very much.. :)
1. A number system in computer programming is a way of representing and expressing numerical values. Computers use different number systems to store and process data.
2. Here are the explanations and steps to convert between different number systems:
- Binary: The binary number system uses only two digits, 0 and 1. Each digit represents a power of 2. To convert binary to decimal, multiply each digit by the corresponding power of 2 and sum them up. To convert decimal to binary, divide the number by 2 repeatedly and record the remainder from each division in reverse order.
Example: Convert binary number 1010 to decimal: (1 x 2^3) + (0 x 2^2) + (1 x 2^1) + (0 x 2^0) = (8 + 0 + 2 + 0 = 10)
- Octal: The octal number system uses eight digits from 0 to 7. Each digit represents a power of 8. To convert octal to decimal, multiply each digit by the corresponding power of 8 and sum them up. To convert decimal to octal, divide the number by 8 repeatedly and record the remainder from each division in reverse order.
Example: Convert octal number 72 to decimal: (7 x 8^1) + (2 x 8^0) = (56 + 2 = 58)
- Hexadecimal: The hexadecimal number system uses sixteen digits from 0 to 9 and A to F. Each digit represents a power of 16. To convert hexadecimal to decimal, multiply each digit by the corresponding power of 16 and sum them up. To convert decimal to hexadecimal, divide the number by 16 repeatedly and record the remainder from each division, replacing any remainder between 10 to 15 with the respective letter (A to F).
Example: Convert hexadecimal number 3A to decimal: (3 x 16^1) + (10 x 16^0) = (48 + 10 = 58)
- Decimal: The decimal number system is the most commonly used number system in daily life. It uses ten digits from 0 to 9. Each digit represents a power of 10.
I hope this helps! Let me know if you have any more questions.
1. A number system in computer programming is a way of representing and manipulating numbers. It defines the set of symbols used to represent numbers and the rules for performing arithmetic operations.
2. Binary, Octal, Hexadecimal, and Decimal (DEC) are different number systems commonly used in computer programming.
- Binary: This is a base-2 number system that uses only two symbols, 0 and 1. Each digit in a binary number is called a "bit" (short for binary digit). To convert binary to other number systems:
- To convert binary to decimal, multiply each bit with the corresponding power of 2 and sum them up.
- To convert binary to octal or hexadecimal, group the bits in sets of 3 or 4 (from the rightmost digit) and convert each group to the respective number system.
- Octal: This is a base-8 number system that uses digits ranging from 0 to 7. Each digit represents three binary digits. To convert octal to other number systems:
- To convert octal to decimal, multiply each digit with the corresponding power of 8 and sum them up.
- To convert octal to binary, convert each digit to its corresponding three-digit binary representation.
- Hexadecimal: This is a base-16 number system that uses digits ranging from 0 to 9 and letters A to F (representing 10 to 15). Each digit represents four binary digits. To convert hexadecimal to other number systems:
- To convert hexadecimal to decimal, multiply each digit with the corresponding power of 16 and sum them up.
- To convert hexadecimal to binary, convert each digit to its corresponding four-digit binary representation.
- Decimal (DEC): This is the most commonly used number system in everyday life, also known as the base-10 system. It uses digits ranging from 0 to 9. To convert decimal to other number systems:
- To convert decimal to binary, repeatedly divide the decimal number by 2 and note down the remainders (from bottom to top).
- To convert decimal to octal or hexadecimal, repeatedly divide the decimal number by 8 or 16 and note down the remainders (from bottom to top). For remainders greater than 9, use letters A to F.
There are online converters and tools available that can help in converting between different number systems. Additionally, software programming languages often provide built-in functions or methods for converting between number systems.