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Number System : Problems on Numbers Video Lecture | CAT Made Easy - Video Lectures by Nishant Sir | IIM K
FAQs on Number System : Problems on Numbers Video Lecture - CAT Made Easy - Video Lectures by Nishant Sir - IIM K
| 1. What are the different types of number systems commonly used in mathematics? |  |
Ans. The most commonly used number systems in mathematics include the natural numbers (N), whole numbers (W), integers (Z), rational numbers (Q), irrational numbers, and real numbers (R). Additionally, there are binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16) systems, each serving specific purposes in computing and mathematics.
| 2. How can I convert a number from decimal to binary? | |
Ans. To convert a decimal number to binary, you can repeatedly divide the number by 2 and record the remainders. For example, for the decimal number 13, divide by 2: 13 ÷ 2 = 6 remainder 1, then 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, and 1 ÷ 2 = 0 remainder 1. Reading the remainders from bottom to top gives you 1101 in binary.
| 3. What is the significance of the binary number system in computer science? | |
Ans. The binary number system is fundamental in computer science because it aligns with the on/off states of electronic circuits. Computers use binary (0s and 1s) to represent data and perform calculations, making it efficient for processing and storing information. Each bit represents a binary digit, allowing complex data structures and instructions to be constructed from simple binary signals.
| 4. How do I determine if a number is rational or irrational? | |
Ans. A number is defined as rational if it can be expressed as a fraction a/b, where a and b are integers, and b is not equal to 0. In contrast, an irrational number cannot be expressed as such a fraction. Common examples of irrational numbers include π and √2, which cannot be represented as a simple fraction and have non-repeating, non-terminating decimal expansions.
| 5. What are some common operations performed with different number systems? | |
Ans. Common operations with different number systems include addition, subtraction, multiplication, and division. For example, in binary, these operations follow specific rules similar to decimal operations but are based on powers of 2. In hexadecimal, calculations are performed using base-16, often requiring conversion to and from decimal when necessary. Understanding these operations is crucial for applications in programming and digital electronics.
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