Paper 1 · ICT
UGC NET June 2024 Re-Exam (22.08.2024) Shift-I
If (L)M represents a number L in the base-M number system, then identify the correct descending order of the following numbers when converted to base-10. Choose the correct answer from the options given below.
- 1. (9C)16
- 2. (233)8
- 3. (313)7
- 4. (10011110)2
A3, 4, 2, 1
B4, 3, 1, 2 ✓ Correct
C2, 3, 1, 4
D4, 3, 2, 1
Correct answer: (B) 4, 3, 1, 2 — The descending order is (10011110)2, (313)7, (9C)16, (233)8, so the answer is 4, 3, 1, 2.
Explanation
★The descending order is (10011110)2, (313)7, (9C)16, (233)8, so the answer is 4, 3, 1, 2.
★Converting each to base 10 makes them comparable.
★(10011110)2 equals 158, the largest.
★(313)7 equals 3 times 49 plus 7 plus 3, which is 157.
★(9C)16 equals 144 plus 12, which is 156.
★(233)8 equals 128 plus 24 plus 3, which is 155, giving 4, 3, 1, 2.
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