If (L) base M represents a number L in base M number system, then identify the correct ascending order of the following numbers 1 to 4, when converted to decimal number system.

1.2) in base 4

2.11) in base 2

3.2) in base 8

4.(3F.6) in base 16

A2, 4, 1, 3

B3, 4, 1, 2 ✓ Correct

C1, 4, 2, 3

D3, 4, 2, 1

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

Explanation

Converting each number to decimal shows number 3 is the smallest at 63.25, so the ascending order begins with it.

Number 3, (77.2) in base 8, equals 63.25 in decimal, the lowest value here.

Number 4, (3F.6) in base 16, equals 63.375, placing it second.

Number 1, (333.2) in base 4, equals 63.5, placing it third.

Number 2, (111111.11) in base 2, equals 63.75, the largest value.

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

The whole parts are all 63, so only the fractional parts separate these values.

Want more like this? Create a free account to practise a full test, track your progress, and get spaced-repetition review.