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Conversions to other Number System- 1 Video Lecture | Quantitative Aptitude (Quant) - CAT

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FAQs on Conversions to other Number System- 1 Video Lecture - Quantitative Aptitude (Quant) - CAT

1. What is a number system and why are conversions to other number systems important?
Ans. A number system is a systematic way of representing numbers using digits or symbols. Conversions to other number systems are important because they allow us to work with numbers in different bases or radices, such as binary, octal, or hexadecimal. This is particularly useful in computer science and digital electronics, where binary is the fundamental number system used to represent information.
2. How do I convert a decimal number to binary?
Ans. To convert a decimal number to binary, you can use the division-by-2 algorithm. Start by dividing the decimal number by 2 and write down the remainder. Then, continue dividing the quotient by 2 until you reach 0, writing down the remainders each time. The binary representation of the decimal number is the sequence of remainders in reverse order.
3. What is the octal number system and how can I convert a decimal number to octal?
Ans. The octal number system uses a base of 8 and uses the digits 0-7 to represent numbers. To convert a decimal number to octal, you can use the division-by-8 algorithm. Divide the decimal number by 8 and write down the remainder. Repeat this process until the quotient is 0, writing down the remainders each time. The octal representation of the decimal number is the sequence of remainders in reverse order.
4. How do I convert a binary number to hexadecimal?
Ans. To convert a binary number to hexadecimal, first group the binary digits into sets of four, starting from the rightmost digit. If the leftmost group has fewer than four digits, add leading zeros. Then, convert each group of four binary digits to its equivalent hexadecimal digit. For example, 0001 is equivalent to 1 in hexadecimal, 1010 is equivalent to A, and 1111 is equivalent to F. Concatenate the hexadecimal digits together to get the hexadecimal representation of the binary number.
5. Can I convert a number from one non-decimal system directly to another non-decimal system?
Ans. Yes, it is possible to convert a number from one non-decimal system directly to another non-decimal system, as long as both systems are powers of the same base. For example, you can convert a binary number to octal by first converting it to decimal and then to octal. However, if the number systems have different bases, you would need to convert to decimal first before converting to the desired number system.
185 videos|158 docs|113 tests

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