15110 Fall 2011 [Cortina/von Ronne]
Written Homework 6  due THURSDAY, October 20 in LAB
Reading Assignment
Read sections 7.17.6
in chapter 7 of the textbook
Explorations in
Computing and chapter 3 of Blown To Bits.
Instructions

Type or neatly write the answers to the following problems.

Please STAPLE your homework before you hand it in.

On the first page of your homework, include your name,
andrew ID, lab section (AN), and the assignment number.

You must hand in your homework at the start of class on the given due date.
Exercises
 (2 pts)
The 8bit value 11100111 might be an unsigned integer,
signed integer, or ASCII character transmitted with even parity.
 What is its value if it is interpreted as an unsigned integer?
Show your work.
 What is its value if it is interpreted as a signed integer?
Show your work.
 What is its value if it is interpreted as an ASCII value
transmitted with even parity? (Note: The parity bit is the leftmost
bit.)
 If the binary value above represented a character and was
transmitted and then received as 11110101, would the
receiver be able to detect the error? Why or why not?
 (1 pt)
Another way to represent unsigned integers is to use a representation
called Binary Coded Decimal (BCD). In this representation, each
decimal digit of an integer is represented using 4 bits as follows:
0 1 2 3 4 5 6 7 8 9
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
 Show how to represent the integer 15110 using BCD.
 If we represent an integer using BCD with 16 bits, what
are the minimum and maximum values that can be stored using
this representation?
 (1 pt)
Show how to represent the binary floating point value
+111.010101 X 2^{24} using the IEEE754 standard
for singleprecision floating point values (using 32 bits).
Show your work.
 (2 pts)
The Rotokas language is spoken in central Bougainville
in Papua New Guinea.
The Rotokas alphabet consists of 12 letters.
The relative frequency of each letter based on a set
of Rotokas text is given below:
A 0.218
E 0.088
G 0.013
I 0.111
K 0.022
O 0.130
P 0.055
R 0.118
S 0.018
T 0.031
U 0.072
V 0.124
 Using RubyLabs, build a Huffman tree using these frequencies.
Draw the resulting tree.
 Using RubyLabs and the tree from part (a), write the Huffman
code assigned to each letter.
 Encode the Rotokas word EKARAU (meaning: sugar cane)
using Huffman codes.
 If we encoded the Rotokas word EKARAU using
a fixed width code, what is the minimum size of the encoded
word in bits? How does this compare to the Huffman encoding?
 (1 pt)
 An image has pixels that use only 128 colors.
What is the minimum number of bits needed to represent
each pixel? Explain your answer.
 Pixels can be represented by specifying the
amount of red (R), green (G), and blue (B) to combine
to obtain the color on a computer screen.
Each of these values can range from 0 to 255, inclusive.
The color sienna has an R value of 160,
a G value of 82, and a B value of 45.
How would this color be represented in a computer
in hexadecimal? (Hint: Convert the values
to binary first.)
 (1 pt)
 If a musical recording is sampled in stereo at a rate
of 44,100 samples per second and each sample is 16 bits,
exactly
how many bytes are required to store 1 minute of this music?
Show your work.

A CD can typically store 700MB of data. If we represent
audio files using the MP3 compression standard using a
bit rate of 160 Kbps (kilobits per second), how many whole
songs can we store in MP3 format
on the CD if each song is exactly
4 minutes long? You may assume the CD has no other information
stored (e.g. index information, titles, etc.).
 (2 pts) Based on Chapter 3 of Blown To Bits, answer the
following questions about data representation.
 Bob highlights a sensitive message in a Word document and changes
its color to white to match the background of the document so others
won't see it. If he sends this document to Alice, does she have the
sensitive information? Why or why not?
 What is spatial coherence and temporal coherence
with respect to images? How does each concept allow us to transmit images
using fewer bits?
 Steganography is the hiding of information within other information.
Using one of the examples given in the chapter as a guide,
find the hidden message in the following announcement:
Important Liability Information: Keep employees
productive! Reduce injuries now. Carefully inspect packages, listing each
sender on formatted cards. On Mondays, please unload trucks inside North
garages.