Wed Feb 8
You have up to 20 minutes. You may use a standard calculator if necessary, but no text book or notes.
+5 Convert the following 6-bit signed two’s complement binary numbers into base ten.
110100
-12 (= -32 + 16 + 4)
001011
11 (= 8 + 2 + 1)
110010
-14 (= -32 + 16 + 2)
101101
-19 (= -32 + 8 + 4 + 1)
+5 Below is a tree representing a variable-width encoding of 9 letters. Use it to:
10111101110011101
into a word: FIGHT
FELT
as bits: 1011101000001
+5 If an image uses 12 bits for each pixel, what is the maximum number of distinct colors it can contain?
\(2^{12} = 4096\) 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.