If (L)M represents a number L in base -M number system, then which of the…

To verify the equalities, we convert 512.125 to each base. Integer Part (512): - Base 2: 512 = 2^9, so it is written as 1000000000. - Base 8: 512 = 8^3, so it is written as 1000. - Base 16: 512 = 2 * 16^2, so it is written as 200. - Base 4: 512 = 2 * 4^4, so it is written as 20000. Fractional Part (0.125): - Base 2: 0.125 = 1/8 = 1/2^3, so it is written as .001. - Base 8: 0.125 = 1/8, so it is written as .1. - Base 16: 0.125 = 2/16, so it is written as .2. - Base 4: 0.125 = 2/16, so it is written as .02. Comparing with options: A. (512.125)10 = (1000000000.001)2 is True. B. (512.125)10 = (1000.1)8 is True. C. (512.125)10 = (200.2)16 is True. D. (512.125)10 = (2000.02)4 is False because the integer part should be 20000. Thus, A, B, and C are correct.