Paper 1 · ICT
UGC NET December 2023 Re-Exam (14.12.2023) Shift-I
Given below are two statements with reference to different number systems. In the light of the above statements, choose the most appropriate answer from the options given below.
- Statement I: (0.6875) in base 10 equals (0.1011) in base 2.
- Statement II: (111011.101) in base 2 equals (58.625) in base 10.
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 0.6875 converts to binary by taking successive fractional doublings.
★This gives 0.1011 in base 2, so Statement I is correct.
★For Statement II, the binary 111011.101 is expanded by place values.
★The integer part gives 59 and the fraction gives 0.625, totalling 59.625, not 58.625.
★Because the stated decimal value is wrong, Statement II is incorrect.
Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.
Shared by Mcqkart · via Mcqkart.in