I just converted the fraction $\frac{3}{5}$ to the following floating point binary number: $(1.001100110011001100110011\cdots)_{2}\times 2^{-1}$.
Now, I am trying to find the two nearest machine numbers to 23 places to the right of the binary point.
The lower bound can be found by simply chopping after 23 places: $x_{\_}=(1.00110011001100110011001)_{2}\times 2^{-1}$.
The upper bound needs to be done by rounding up, but how do I round up $(1.001100110011001100110011\cdots)_{2}\times 2^{-1}$ to 23 places? Pleaes help - I am not yet comfortable working in binary.