Number System — Computer Awareness

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Number System

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Q.1

WBCS Prelims 2021

The binary equivalent of decimal number 4.625 is

A. 100.001

B. 100.110

C. 100.101

D. 100.011

Explanation

Core Formula/Logic: Convert integer part by repeated division by 2, fractional part by repeated multiplication by 2.
Step-by-Step Solution: 1. Integer part: 4 ÷ 2 = 2 remainder 0.
2 ÷ 2 = 1 remainder 0.
1 ÷ 2 = 0 remainder 1.
Read remainders backward: 100.
2. Fractional part: 0.625 × 2 = 1.25 → integer part 1, new fraction 0.25.
0.25 × 2 = 0.5 → integer part 0, new fraction 0.5.
0.5 × 2 = 1.0 → integer part 1, new fraction 0.
Read integer parts forward: 101.
3. Combine: 100.101.
Common Pitfall: Incorrect integer conversion yields 100.001 (option A). Wrong fractional multiplication sequence gives 100.110 (option B) or 100.011 (option D).
Shortcut/Takeaway: Recognize 0.625 = 5/8 = 1/2 + 1/8 = 0.5 + 0.125. In binary, 0.5 is 2^-1 (0.1) and 0.125 is 2^-3 (0.001), so .101 directly.

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Q.2

WBPSC Miscellaneous Prelims 2023

Which number system is often used in computing and programming?

A. Binary

B. Hexadecimal

C. Octal

D. Decimal

Explanation

Why Correct: Binary (base-2) is the fundamental number system in computing because computer hardware uses two voltage states (0 and 1) to represent data and execute instructions. All higher-level number systems are derivatives of binary for human readability.
Distractor Analysis: Hexadecimal (base-16) is used for memory addressing and color codes but is not the primary internal system. Octal (base-8) was historically used in early computing but is now rare. Decimal (base-10) is the human-centric system and is not directly used by computer logic circuits.
Takeaway: In exams, remember that binary is the only system directly processed by the CPU; hexadecimal and octal are compact representations of binary, and decimal is for input/output only.

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