Given a value is represented by the following base-10 number:

v=13.788

What is the binary number that represents a value that is closest to v, given that the binary number has 5 bits to the left of the decimal (binary) point and 3 bits to the right of the decimal (binary) point? In other words, the binary number looks like the following:

b 4 b 3 b 2 b 1 b 0 . b 1 b 2 b 3

Enter your binary number in the space provided.

A trick to do this is to express 13.788 in rounded units of 2 3. If 13.788 m 2 3, then convert m to a binary number. Keep in mind, however, that each unit is 2 3, so the binary point needs to be shifted to the left accordingly.

For example, let's say the v = 100010 2 2 3, then v = 10001.0 2 2 2, and v = 1000.10 2 2 1. The bottom line is that we need to completely get rid of the power-of-2 multiplier so the value v is expressed solely as a binary number.

____________