Computer science

ECE 5484 (Fall 2019)  Homework 3 Page 1 of 2

Virginia Tech  ECE 5484: Fundamentals of Computer Systems  Fall 2019

Homework 3 Assignment (Problem 1 updated 9/20/19)

Before you start this homework assignment, please be sure that you have completed all of the

following activities.

 Complete the required readings for this module, and view the associated online

lectures before or while you work on this homework assignment.

 Note the grading policies, including policies for submitting assignments, in the syllabus.

 Review the course schedule. Note the due dates for course assignments.

Please note the following.

 All submissions of graded work in this class are subject to the Graduate Honor System.

 Solutions must be clear and presented in the order assigned. Solutions must show work

needed, as appropriate, to derive your answers. Written answers should be concise, but

sufficiently complete to answer the question. Neat hand drawings, where needed, are

acceptable. Your final solution for each problem must be easily identified. Show your

work for full credit.

 At the top of the first page, include: your name (as recorded by the university); your

email address; and the assignment name (e.g., “ECE 5484, Homework 3”). Do not

include your Virginia Tech ID number or your Social Security Number.

 Homework must be submitted as a PDF (.pdf) file with the file name

lastname_firstname_HW3.pdf, where lastname is your last or family name and

firstname is your first or given name. Submit a single file unless an additional file is

explicitly requested.

 Submit your assignment using the Assignments area of the class website. You must

submit your assignment by 11:55 p.m. on the due date.

Homework 3 consists of the following problems.

Problem 1. How many bits are required to address a 4M × 16 main memory under the

following conditions. (“4M x 16” means there are 4x220 16-bit words.)

a) The main memory is byte-addressable?

b) The main memory is word-addressable? (For part b, assume a 16-bit word.)

Problem 2. You want to use 256 x 8 RAM chips to provide a memory capacity of 8,192 bytes.

(Yes, this is a ridiculously small RAM chip and memory capacity by today’s standards, but it

keeps the problem simple.)

a) How many chips will you need?

b) How many bits will each address contain?

c) How many address lines must go to each chip?

d) How many address lines must be decoded for the chip select inputs? In other words,

specify the size of the decoder.

ECE 5484 (Fall 2019)  Homework 3 Page 2 of 2

Problem 3. A digital computer has a memory unit with 32 bits per word. The instruction set

consists of 122 different operations. All instructions have an operation code part (opcode) and

an address part (allowing for only one address). Each instruction is stored in one word of

memory.

a) How many bits are needed for the opcode?

b) How many bits are left for the address part of the instruction?

c) What is the maximum allowable size for memory?

d) What is the largest unsigned binary number that can be accommodated in one word of

memory?

Problem 4. Section 4.10 of the text provides an example of the execution of a simple MARIE

program.

For this problem, you are to complete a similar example for a different program. In particular,

for the MARIE program given below, you are to complete the equivalent of Figure 4.14, but for

the program below. You do not need to show how the “Halt” instruction is executed. Specify

values in PC, IR, MAR, MBR, and AC in hexadecimal. A template for your answer is provided as

a Microsoft Word file that is included with this assignment on the class Canvas site. You are to

incorporate your answer for this problem into your submission for the homework assignment

so that you submit only one PDF file for the entire assignment.

The program is as follows. Note that this table is the equivalent of Table 4.3 in the textbook,

only for a different program.

Hex

Address Instruction

Binary Contents of

Memory Address

Hex Contents

of Memory

100 Load 105 0001 0001 0000 0101 1105

101 Subt 104 0100 0001 0000 0100 4104

102 Store 104 0010 0001 0000 0100 2104

103 Halt 0111 0000 0000 0000 7000

104 00A3 0000 0000 1010 0011 00A3

105 00F3 0000 0000 1111 0011 00F3

Problem 5. It is the next installment of the ECE 5484 Scavenger Hunt! Two pioneers of early

computers and computer organization were Howard H. Aiken and John von Neumann. Answer

the questions below regarding Aiken and von Neumann. Cite sources used for your answers.

a) Is Aiken or von Neumann associated with the so-called Princeton architecture?

b) Is Aiken or von Neumann associated with the so-called Harvard architecture?

c) Briefly, and in your own words, what is the key feature of a Princeton architecture

computer compared to the Harvard architecture?

d) Does the MARIE architecture owe more to Aiken or von Neumann? In your own words,

briefly justify your answer.