FAQs on Basics of Number System

Question 1

1. What's the difference between decimal and binary number systems?

Accepted Answer

Ans. Decimal uses base-10 with digits 0-9, while binary uses base-2 with only 0 and 1. Decimal is standard for daily counting; binary forms the foundation of computer operations and digital electronics. Understanding both systems is essential for GATE General Aptitude, as conversions between them frequently appear in exams.

Question 2

2. How do I convert a number from one base to another quickly?

Accepted Answer

Ans. To convert to decimal, multiply each digit by its positional value (base raised to power) and sum them. To convert from decimal, repeatedly divide by the target base and collect remainders in reverse order. Practice with octal and hexadecimal conversions strengthens problem-solving speed for GATE Mechanical Engineering aptitude sections.

Question 3

3. Why do some numbers become non-terminating decimals in certain bases?

Accepted Answer

Ans. A fraction terminates in a base only if its denominator contains only prime factors of that base. In base-10, 1/4 terminates (2² divides 10), but 1/3 doesn't (3 doesn't divide 10). This concept explains why the same fraction behaves differently across number systems-critical for understanding number system fundamentals in competitive exams.

Question 4

4. What are significant figures and why do they matter in calculations?

Accepted Answer

Ans. Significant figures indicate precision in measurements-all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point count. They prevent false accuracy claims in scientific calculations. Mastering significant figures ensures correct representation in engineering problems and aptitude sections requiring numerical precision.

Question 5

5. How do octal and hexadecimal systems help in computer representation?

Accepted Answer

Ans. Octal (base-8) and hexadecimal (base-16) compress binary code into shorter, readable forms-three binary digits equal one octal digit, four equal one hexadecimal digit. Engineers use hexadecimal for memory addresses and digital systems. This conversion skill directly supports questions on data representation in GATE General Aptitude number system topics.

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06:12	Question 2
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41:54	Question 4