If (L)M represents a number L in the base-M number system, then which of the following equalities are true? Choose the most appropriate answer from the options given below.

1.125)10 = (1111111.001)2

2.125)10 = (1333.02)4

3.125)10 = (177.1)8

4.125)10 = (7F.2)16

A1 only

B1 and 2 only

C1, 2 and 3 only

D1, 2, 3 and 4 ✓ Correct

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

Explanation

All four equalities are correct, as 127.125 in decimal converts exactly into each of the listed bases.

In binary 127 is 1111111 and the fraction 0.125 is 0.001, giving 1111111.001.

In base four 127 is 1333 and 0.125 is 0.02, giving 1333.02.

In octal 127 is 177 and 0.125 is 0.1, giving 177.1.

In hexadecimal 127 is 7F and 0.125 is 0.2, giving 7F.2.

The fraction 0.125 is one eighth, which lands neatly in each of these bases.

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