If (L) base M represents a number L in base M number system, then identify the correct descending order of the following numbers when converted to decimal number system.

1.2) in base 4

2.11) in base 2

3.2) in base 8

4.6) in base 16

A2, 4, 3, 1

B1, 3, 4, 2 ✓ Correct

C3, 1, 2, 4

D4, 2, 3, 1

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

Explanation

Converting each number to decimal shows number 1 is the largest at 778.5, so the descending order begins with it.

Number 1, (30022.2) in base 4, equals 778.5 in decimal, the highest value here.

Number 3, (777.2) in base 8, equals 511.25, placing it second.

Number 4, (197.6) in base 16, equals 407.375, placing it third.

Number 2, (10000110.11) in base 2, equals 134.75, the smallest value.

The correct descending order is therefore 1, 3, 4, 2.

The fractional part is read as digits divided by successive powers of the base.

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