Wed Feb 11

You have up to 20 minutes. You may use a standard calculator if necessary, but no text book or notes.

+5 Below is a tree representing a variable-width encoding of 9 letters. Use it to:

- decode the bits
`10011111010011010`

into a word:`WHINE`

- encode the word
`WITH`

as bits:`100110101111`

- decode the bits
+5 Decode the following 8×8 image indicated by the hexadecimal number along the right side, which uses 1 bit per pixel.

+5 If an image uses 9 bits for each pixel, what is the maximum number of distinct colors it can contain?

\(2^9 = 512\) colors

+5 Draw a tree representing a

**variable-width**encoding of the four letters**A, L, N,**and**T.**Use it to encode the word`ATLANTA`

. The fixed-width tree (below) uses exactly 2 bits per character, so encoding`ATLANTA`

requires 14 bits. How many bits does your tree need to encode`ATLANTA`

?Here is one possible solution. In this tree, L and N are extended to 3 bits each, so that A can be just 1 bit. We can then encode ATLANTA as 13 bits.