Assignment 2

Reading Assignment: Notes for Week 2. Review your notes on C programming, in particular on array and pointer.

1. For problems 1-4 below, assume 4-bit words and integers represented in 2's complement form.

A. (6 points) Which of the following binary numbers are negative?
a.) 1100 b.) 0101 c.) 1001

B. (6 points) Negate the following numbers:
a.) 0001 b.) 1010 c.) 1001

C. (6 points) Give the binary representation for:
a.) -7 b.) -1 c.) 7

D. (12 points) Perform the following operations and indicate, in each case, whether or not overflow occurs:
a.) 1000 b.) 1000 c.) 1111 d.) 0000
+0001 +1111 -0001 -1111

2. (10 points) An expedition to Mars found the ruins of a civilization. The explorers were able to translate the
    mathematical equations:
                5x² -50x + 125 = 0
    with the solutions:
                x = 5    and    x = 8.
    The x = 5 solution seemed okay, but x = 8 was puzzling. The explorers reflected on the way
    in which Earth's number system developed. How many fingers would you say the Martians had?

3. (15 points) Suppose Venetians use a trinary number system with their three digits defined as follows:
        X    denotes    +1
        Y    denotes      0
        Z    denotes     -1

Numbers in their system consist of four trinary digits with the value of the number B3B2B1B0 given
by the expression: 27*B3 + 9*B2 + 3*B1 + B0. For example, XZYX = 19.

a.) What values does ZYYX represent?

b.) How do Venetians represent +30?
How do they represent -30?

c.) How many different values can Venetians represent in their system?

        d.) Suppose MAX is the largest positive integer Venetians can represent in their system. Can
             they represent all integers in the range from 0 to MAX, inclusive? What about from -MAX to
             0, inclusive?

4. (15 points) Given the following function prototype in C, answer i. – iv. below:

unsigned char Read_Results (char * pResults, char byArray[], int pos);

a. What is the size in bytes of the return value of the function? _________

b. What is the size in bytes of each of the parameters passed to the function?

_________ char *pResults

_________ char byArray[]

_________ int pos

c. Write a C statement that reads the data at address (pResults+pos) and assigns it to the element of byArray at position pos.

5. (20 points) Given the C variable declarations, place the variables into memory locations in the table below. Put the name of the variable into any memory location that it uses. Place an X in any unused location.

char a[5];

short b;

short c;

int d;

long e;

short f;

char *g;

Assume that the block of variables is allocated in memory beginning at address 0x30001000. That is, the address of variable “a” is 0x30001000.

Assume also:

byte-ordering is big endian (big byte first, i.e., MSB at lower address)
memory addresses are 32 bits
int data type is 32 bits
variables must satisfy alignment requirements (word alignment for 32-bit data types and half-word alignment for 16-bit data types).

Address	Each column is one byte. Thus, a row is a double word.
0x30001000
0x30001008
0x30001010
0x30001018

i. How many bytes of memory are used for this block of variables? ______

ii. What is the address of variable “e”? ________________________

iii. What is assigned to variable “g” in each of the following statements?

g = a; _____________________

g = &a[5]; _____________________

6. (10 points) Given the memory dump and declarations, answer the following questions.

Address (hex) Memory Contents (hex)

30005000 00 FE 25 24 5B 1A EE 05

30005008 AC AE 81 83 30 00 32 00

30005010 30 00 50 04 AC CB F0 8D

short a[7];

char b;

short * c;

Assume that the variables a, b and c are allocated in memory beginning at address 0x30005000. That is, the address of “a” is 0x30005000; “b” follows “a” in memory; and “c” follows “b”.

i. What is the value of *(c + 2): _______________________

ii. What is the value of b after executing the statement: _______________________

c = &a[3];