Paper 1 · ICT
UGC NET December 2023 (14.12.2023) Shift-II
Given below are two statements with reference to number systems. In the light of the above statements, choose the most appropriate answer from the options given below.
- Statement I: (0.5625) in base 10 equals (0.9) in base 16.
- Statement II: (0.3) in base 10 equals (0.4BBB…) in base 16.
ABoth Statement I and Statement II are correct
BBoth Statement I and Statement II are incorrect
CStatement I is correct but Statement II is incorrect ✓ Correct
DStatement I is incorrect but Statement II is correct
Correct answer: (C) Statement I is correct but Statement II is incorrect — Statement I is correct but Statement II is incorrect, so that is the answer.
Explanation
★Statement I is correct but Statement II is incorrect, so that is the answer.
★Decimal 0.5625 in binary is 0.1001, which groups into the hex digit 9.
★So 0.5625 equals 0.9 in base 16, making Statement I correct.
★Decimal 0.3 does not give a clean 0.4BBB pattern in hexadecimal.
★Its correct hexadecimal expansion repeats a different digit sequence, not 4BBB.
★Because the stated hex value is wrong, Statement II is incorrect.
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