Quiz 2 Solutions

Wed Feb 10

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

  1. +5 Convert the following 5-bit signed two’s complement binary numbers into base ten.

    1. 11100    = \(-4\), because it’s \(-16+8+4\)
    2. 00111    = \(+7\), because it’s \(4+2+1\)
    3. 11010    = \(-6\), because it’s \(-16+8+2\)
    4. 11001    = \(-7\), because it’s \(-16+8+1\)

  1. +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

  1. +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. Note this has little to do with color; when you want to represent anything in 9 bits, there are \(2^9\) possible things. Could be characters, numbers, student IDs, etc.

  1. +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?

    A fixed-width encoding of four letters.

    A fixed-width encoding of four letters.

    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.

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