Given below are two statements with reference to different number systems:…
2023
Given below are two statements with reference to different number systems:
Statement I: (0.6875)10 = (0.1011)2
Statement II: (111011.101)2 = (58.625)10
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer: C. Statement I is correct but Statement II is incorrect — CONCEPTIn a positional number system, each digit contributes digit × base raised to its position. Positions to the left of the radix point use non-negative…
- A.
Both Statement I and Statement II are correct
- B.
Both Statement I and Statement II are incorrect
- C.
Statement I is correct but Statement II is incorrect
- D.
Statement I is incorrect but Statement II is correct
Attempted by 13 students.
Show answer & explanation
Correct answer: C
CONCEPT
In a positional number system, each digit contributes digit × base raised to its position. Positions to the left of the radix point use non-negative powers; positions to the right use negative powers. A conversion is valid only when both numerals have the same positional-value sum.
APPLICATION
Expand Statement I: (0.1011)2 = 1×2-1 + 0×2-2 + 1×2-3 + 1×2-4 = 0.5 + 0 + 0.125 + 0.0625 = 0.6875.
Expand Statement II: (111011.101)2 = 1×25 + 1×24 + 1×23 + 0×22 + 1×21 + 1×20 + 1×2-1 + 0×2-2 + 1×2-3 = 32 + 16 + 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125 = 59.625.
CROSS-CHECK
Converting 58.62510 in the other direction gives 5810 = 1110102 and 0.62510 = .1012, so 58.62510 = 111010.1012, not 111011.1012.
RESULT
Statement I is correct, whereas Statement II is incorrect.