Consider converting y=(0.6875)10=(0.1011)2 with only L=2 bits reserved for the fractional part. In this case, both the basic and base expansion algorithm would yield (0.10)2=(0.5)10; however, the sum of the remaining powers of two indicate that the closest approximation should be (0.75)10=(0.11)2. Hence, the algorithm presented above does not round up based upon the value of the next binary digit associated with the next lower power of 2. Try to modify the approach presented by adding some steps that will inspect the next lower power of 2 and round the number accordingly.