CS 255  Computer Organization/Architecture I
Homework Assignment 1
Due date: See Class Webpage
1. 2's Complement Encoding (20 pts)
A computer X uses 2bytes
to store the values in this question.
Furthermore,
the computer uses the 2's complement number system
to represent signed numbers.
Each question is 5 pts.
 What are the 2's complement representation for the values
4317_{(10)} and −4317_{(10)}
in computer X ?
 What decimal values are represented by the following
patterns in computer X ?
Pattern 1: 0000 0010 0100 0101
Pattern 2: 1111 0001 0101 0111
 Give the binary pattern that results from adding
the two patterns in part 2.
What value is represented by this pattern ?
 Give the binary pattern that results from subtracting
the pattern 1 from pattern 2 in part 2.
What value is represented by this pattern ?

2. 10's Complement Encoding (20 pts)
Consider the 10's complement encoding scheme using 4 digits.
Each question is 5 pts.
 What are the 10's complement representation for the value
3429 and −3429 ?
 What value is represented by 8896 ?
 Add the representations 9765 and 9995.
(Truncate the result to 4 digits !)
What value is represented by the result ?
Did the addition resulted in the correct value ?
 Multiply the representations 9765 and 9995.
(Truncate the result to 4 digits !)
What value is represented by the result ?
Did the multiplication resulted in the correct value ?

3. Binary Arithmetic (10 pts)
Do the following arithmetic computations in binary.
 11110101 x 1101
Show the complete tail multiplication to get full credit
 11110101 / 1101
Show the give complete division to get full credit
4. Base5 Arithmetic (10 pts)
5. Octal, Hexadecimal and Other Numbers (20 pts)
 Give the representation of the value 4539 in the octal number system
(that is based on the number 8).
 Give the representation of the value 4539 in the hexadecimal number system
(that is based on the number 16).
 Give the representation of the value 4539 in the "nano number system"
(that is based on the number 9).
 Give the representation of the value 4539 in the "13 number system"
(that is based on the number 13; use A to represent 10, B for 11 and C
for 12).
6. Encoding (20 pts)
Show the binary representation (in bits) for the following
data items when they are stored in computer memory:
 The string "Huh?"
 The string "x=52;"
 The pattern stored in a byte typed variable by the
statement x=52;
 The string "x=0;"
 The pattern stored in an int typed variable by the
statement x=0;
 The octal number 123057
 The hexadecimal number BAD4
 The single precision float point number 4.0
in IEEE 754 representation
 The single precision float point number 7.75
in IEEE 754 representation
 What is the float point number (written in decimal) represented by the
following IEEE 754 representation:
11000001010001000000000000000000


Extension request
Statement of Policy on Homework Assignments
Students will be graded partially on the basis of their
homework assignments. These homework
assignments are to be treated as examinations, and are
expected to be your individual work. While
discussions with other students in the course may be
permitted or encouraged by your instructor, you
should write your program yourself.
Your instructor (and any teaching assistants assigned to
the course) will be glad to help you to the extent
that he or she feels reasonable.
Submissions based on other students solutions in prior
offerings of the course specifically violate these
guidelines, as do submissions prepared with the help of an outside "tutor".
You should take precautions to protect the confidentiality
of your work, do not collaborate on questions that you turn in
for a grade, do not show your solution to a fellow student,
not even after the due date for some students may have
receive extension.
All submissions should include a comment statement near
the top of the program of the form:
THIS CODE IS MY OWN WORK, IT WAS WRITTEN WITHOUT CONSULTING
A TUTOR OR CODE WRITTEN BY OTHER STUDENTS  your name
Cases of apparent plagiarism or collusion will be referred
to the Honor Council.