Paper 1 · ICT
UGC NET June 2024 Re-Exam (22.08.2024) Shift-II
If (L)M represents a number L in the base-M number system, then which of the following equalities are true? Choose the correct answer from the options given below.
- 1. (512.125)10 = (1000000000.001)2
- 2. (512.125)10 = (1000.1)8
- 3. (512.125)10 = (200.2)16
- 4. (512.125)10 = (2000.02)4
A1 and 2 only
B1 and 3 only
C2, 3 and 4 only
D1, 2 and 3 only ✓ Correct
Correct answer: (D) 1, 2 and 3 only — The true equalities are 1, 2 and 3, so the answer is 1, 2 and 3.
Explanation
★The true equalities are 1, 2 and 3, so the answer is 1, 2 and 3.
★The integer 512 converts to 1000000000 in binary, 1000 in octal and 200 in hexadecimal.
★The fraction 0.125 converts to .001 in binary, .1 in octal and .2 in hexadecimal.
★So statements 1, 2 and 3 correctly represent 512.125 in those bases.
★In base 4, 512.125 does not equal 2000.02, so statement 4 is wrong.
★So the correct equalities are 1, 2 and 3.
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