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Here X1 is represented in Binary and X2 in Hexadecimal.

taking X1 : (23.6)_{10} -----> 23 can be easily converted to binary as = (10111)_{2}

**now for decimal values... **

1)multiply mantissa by 2

2)record the characteristics and remove from the new value.

3)repeat step 1 and 2 until mantissa is 0. or as per your need.

** for .6 **

1).6*2 = 1.2

2) characteristic(**c1**) =1 mantissa(**m1**) = .2

simlarly we will get** c2**=0 **M2**=.4 :: **c3**=0 **m2**=.8 :: **c4**=1 **m4**=.6 ::** c5**=1 **m5**=.2 . so value becomes (**10111.1001100110011....**)_{2 }

X1 is recurring value 0011 .

now for **X2**=(**65.535**)_{10}

65 can be easily represented as (41)_{16} now for mantissa repeat the above steps but instead of 2 multiply mantissa by 16(for hexadecimal)

**m1**=8 **c1**=.56 :: **m2**=8 **c2**=.96 :: **m3**=15(F) **c3**=.36 :: **m4**=5 **c4**=.76 :: **m5**=12(C) **c5**=.16 :: m6= 2 c6= .56 :: m7= 8 c7= .96

so X2= (**41.88F5C28F5C28.....**)_{16}

X2 is recurring value F5C28

so it matches with **option D.**

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