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Practice Questions for Number Systems Part-3 Video Lecture | Additional Study Material for UPSC
FAQs on Practice Questions for Number Systems Part-3 Video Lecture - Additional Study Material for UPSC
| 1. What are the different number systems used in mathematics? |  |
Ans. In mathematics, there are several different number systems used, including the decimal system (base-10), binary system (base-2), octal system (base-8), and hexadecimal system (base-16). Each number system has its own set of digits and rules for representing and manipulating numbers.
| 2. How do you convert a decimal number to a binary number? | |
Ans. To convert a decimal number to a binary number, you can use the process of successive division by 2. Start by dividing the decimal number by 2 and recording the remainder. Then, divide the quotient obtained by 2 again and record the remainder. Continue this process until the quotient becomes 0. The binary number is obtained by writing the remainders in reverse order.
| 3. What is the significance of the base in number systems? | |
Ans. The base of a number system determines the number of unique digits used in that system and the value assigned to each digit. For example, in the decimal system (base-10), there are 10 unique digits (0-9) and each digit represents a multiple of powers of 10. The base also affects the positional value of digits. Higher bases, such as binary (base-2) or hexadecimal (base-16), require more digits to represent numbers compared to lower bases like decimal.
| 4. How do you convert a binary number to a decimal number? | |
Ans. To convert a binary number to a decimal number, multiply each digit of the binary number by the corresponding power of 2 and sum up the results. Start from the rightmost digit of the binary number, with the power of 2 starting from 0 and increasing by 1 for each subsequent digit.
| 5. What is the octal system and how is it used in computing? | |
Ans. The octal system is a number system with a base of 8, meaning it uses 8 unique digits (0-7). In computing, octal numbers are used to represent groups of three binary digits, as each octal digit can be mapped to a sequence of three binary digits. This makes it easier to represent and manipulate binary numbers in a more compact form. Octal numbers are commonly used in computer programming and hardware design.
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