If (L)M represents the number L in a base-M number system, identify the correct ascending order of the following numbers when converted to decimal. Choose the correct answer from the options given below.

1.base 4

2.base 2

3.base 6

4.base 3

A2, 1, 3, 4

B1, 3, 4, 2

C1, 2, 4, 3

D2, 1, 4, 3 ✓ Correct

Correct answer: (D) 2, 1, 4, 3

Explanation

The correct ascending order in decimal is Statement 2, then Statement 1, then Statement 4, then Statement 3.

Statement 1, (102) in base 4, equals 16+0+2 = 18.

Statement 2, (10001) in base 2, equals 16+1 = 17, the smallest value.

Statement 3, (103) in base 6, equals 36+0+3 = 39, the largest value.

Statement 4, (201) in base 3, equals 18+0+1 = 19.

Ordering 17, 18, 19, 39 gives the sequence 2, 1, 4, 3.

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