ECE 190 Midterm Exam 1 Spring 2011

Practice exam, February 2011

Name: NetID:

Programming studio section (mark only the one you attend):

DCL 440 DCL 520

9:00 AM [ ] AD4 [ ] AD6

12:00 PM [ ] AD5 [ ] AD8

1:00 PM [ ] AD3 [ ] AD7

2:00 PM [ ] AD9

3:00 PM [ ] AD1 [ ] AD2

Be sure your exam booklet has 5 pages.

Do not tear the exam booklet apart.

Write your name at the top of each page.

This is a closed book exam.

You may not use a calculator.

You are allowed one handwritten 8.5 x 11" sheet of notes.

Absolutely no interaction between students is allowed.

Be sure to clearly indicate any assumptions that you make.

Don’t panic, and good luck!

Problem 1 10 points _______________________________

Problem 2 5 points _______________________________

Problem 3 10 points _______________________________

Problem 4 5 points _______________________________

Total 30 points _______________________________

Page: 2 Name: ___________________________________________

Problem 1 (10 points): Binary representation

Part A (2 points): What range of decimal numbers can be represented using 9 bits in each 2’s

complement, 1’s complement, and unsigned binary representations?

2’s complement: _____________________

1’s complement: _____________________

Unsigned binary: _____________________

Part B (2 points): Base 8 representation of numbers is called “octal”, and uses only digits 0

through 7. Give the following equivalent numbers for octal number 1275 in each binary,

decimal, and hexadecimal representation.

Binary: _____________________

Decimal: _____________________

Hexadecimal: _____________________

Part C (1 point): How is the number 2

represented in the floating point data type format?

Answer: _________________________________________________

Part D (1 points): What is the largest possible positive number that can be expressed in the

floating point data type, using an exponent between 1 and 254? Write your answer in binary, in

IEEE 754 floating point format.

Answer: _________________________________________________

Part E (4 points): Using 2-complement arithmetic, what 32-bit number can be added to this

floating point number to effectively multiply by 28?

0 01111101 00000000000000000000000

Answer: _________________________________________________

Page: 3 Name: ___________________________________________

Problem 2 (5 points): Digital logic

Part A (3 points): Using NAND gates only, draw circuits that implement AND and OR gates

AND

OR

Part B (1 points): Using exactly one logic gate whose inputs are not inverted, draw a circuit

equivalent to the given circuit

Part C (1 points): One way to think of logic gate types is to consider what input states guarantee

a certain output state. For example, we could describe the function of an AND gate as “Any low

input guarantees a low output.” Identify what type of gate is represented by the following

phrase: “Any low input guarantees a high output.”

Answer: ____________________________

Page: 4 Name: ___________________________________________

Problem 3 (10 points): Memory Given four 1-bit memory cells, build a 2x2-bit memory unit using only AND, OR, NOT gates

and MUXes:

Page: 5 Name: ___________________________________________

Problem 4 (5 points): C language

Part A (1 points): Assume variables x, y, and z are already declared. Write a C expression to

evaluate 𝑥 + 1

1 + 𝑦𝑧5

Do not switch the order of operands.

Answer: ___________________________________________________

Part B (2 points): Fill in missing expressions to implement the following formula:

𝑓 = {𝑥 𝑓𝑜𝑟 𝑥 ≤ 100 𝑥 𝑓𝑜𝑟 10 < 𝑥 ≤ 100𝑥 + 1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

if ( _________________________________________ )

f = x;

else if ( ____________________________________ )

f = -x;

else

f = x + 1;

Part C (1 points): Write the output produced by the following code segment:

int x = 5;

do {

printf(“%d “, --x);

} while (x != 4)

Answer: ____________________________________________

Part D (1 points): Using only declared variables, write missing arguments in printf function

call that correspond to the provided format conversion specifications.

int count;

char inchar;

printf(“%c %d”, _________________________________________ );

Page: 6 Name: ___________________________________________

Programming Problem

In this assignment, you will need to write a program to calculate π by a Monte Carlo method. The idea of

the Monte Carlo method for computing π is to throw darts at a 2D board. As such, each dart will have an

x coordinate and a y coordinate of the point where it lands. You will then calculate what fraction of darts

falls within a circle with center (0,0) and radius 1. Remember that the point (x,y) is distance √𝑥 + 𝑦

from the origin (0,0). If you throw 100+ darts in this manner, the fraction of darts hitting the unit circle

should start to approximate π/4≈0.785398163.

Your program will first request how many darts you will throw. It will then loop through each dart,

prompting "x and y for dart i? " where i is the number of the current dart, starting from 0. Finally, your

program should output "You hit the unit circle j times." followed by a newline, where j is the number of

darts that landed in the circle.

Here is a sample run:

How many darts? 10

x and y for dart 0? -0.233169 -0.866316

x and y for dart 1? -0.999984 -0.736924

x and y for dart 2? 0.511211 -0.082700

x and y for dart 3? 0.065534 -0.562082

x and y for dart 4? -0.905911 0.357729

x and y for dart 5? 0.358593 0.869386

x and y for dart 6? -0.232996 0.038833

x and y for dart 7? 0.661931 -0.930856

x and y for dart 8? -0.893077 0.059400

x and y for dart 9? 0.342299 -0.984604

You hit the unit circle 7 times

You may NOT use any functions from math.h, such as sqrt.

NOTE: For testing purposes, you can generate x and y coordinates on the interval [-1, 1] by writing at the

top of your program

#include <stdlib.h>

#define FRAND (rand()/(RAND_MAX/2.0)-1.0)

and using "x = FRAND;" to obtain a new random number to assign to x instead of using scanf to

obtain this value form user. Do not forget to remove this test code when turning in your final program!

Name your program file exam1.c. You should compile your code as follows:

gcc -g -Wall -Werror -ansi exam1.c -o test

Make sure your program compiles and works before your turn it in. We will not grade a program that

does not compile and you will lose points if the program compiles with warnings. You obviously will not

receive any points if your program does not do what it is supposed to do. Both functionality and coding

style will be graded, with most points given for functionality and some points given for style. No style

grading will be done if the program does not compile. To turn in the program, execute

handin --EX 1 exam1.c