If (L) in base M represents a number L in base-M number system, then which of the following numbers are equivalent to (AD) in base 16 ?

1.in base 8

2.in base 2

3.in base 10

4.in base 5

A1, 3 & 4 only

B2 & 4 only

C1 & 2 only

D1, 2 & 3 only ✓ Correct

Correct answer: (D) 1, 2 & 3 only

Explanation

The hexadecimal value (AD) equals 173 in decimal, so any number that also converts to 173 is equivalent.

Number 1, (255) in base 8, equals 173 in decimal, so it matches.

Number 2, (10101101) in base 2, equals 173 in decimal, so it matches.

Number 3, (173) in base 10, is already 173, so it matches.

Number 4, (1141) in base 5, equals 171, which is not 173, so it does not match.

The equivalent numbers are therefore 1, 2 and 3 only.

Converting to a common base is the reliable way to compare values across number systems.

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