Which of the following is a binary representation of the base-10 fraction $$93/128$$?

A.   0.1011100
B.   0.1011101
C.   0.1011110
D.   0.1011111

To convert our fraction from a base-10 fraction to a base-2 fraction, let's first write it out in its decimal equivalent:

$\frac{93}{128}=.7265625$

Next, we want to multiply our base 10 decimal by our intended base, 2. We will keep track of the number before the decimal (0 or 1) and take the number after the decimal, the remainder, and multiply it by 2 again. We will do this until we have no remainder:

$$\begin{gathered} .7265625 x 2 = 1.453125. \mathbf{1} carries, .453125 is the remainder \\ .453125 x 2 = 0.90625. \mathbf{0} carries, .90625 is the remainder \\ .90625 x 2 = 1.8125. \mathbf{1} carries, .8125 is the remainder \\ .8125 x 2 = 1.625.\mathbf{ }\mathbf{1} carries, .625 is the remainder \\ .625 x 2 = 1.25. \mathbf{1} carries, .25 is the remainder \\ .25 x 2 = 0.5. \mathbf{0} carries, .5 is the remainder \\ .5 x 2 = 1. \mathbf{1} carries, 0 is the remainder \end{gathered}$$

We now write out our 1 or 0 values from top to bottom behind a leading 0. to get our final binary answer: 0.1011101 (Answer B)