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.