If (L)ₘ represents a number L in base-M number system, then identify the correct descending order of the following numbers 1-4 when converted to decimal number system. Choose the correct answer from the options given below :
1.2)₄
2.11)₂
3.2)₈
4.(C2.6)₁₆
A2, 3, 4, 1
B4, 1, 2, 3
C1, 3, 4, 2 ✓ Correct
D3, 4, 1, 2
Correct answer: (C) 1, 3, 4, 2
Explanation
Converting each number to decimal shows number 1 is the largest at 515.5, so the descending order begins with it.
Number 1, (20003.2) in base 4, equals 515.5 in decimal, the highest value here.
Number 3, (732.2) in base 8, equals 474.25, placing it second.
Number 4, (C2.6) in base 16, equals 194.375, placing it third.
Number 2, (111111.11) in base 2, equals 63.75, the smallest value.
The correct descending order is therefore 1, 3, 4, 2.
Comparing values is easiest once every number is expressed in the same decimal base.
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