Question Description

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COMPUTER SCIENCE 2A

INTRODUCTION TO COMPUTERS

ASSIGNMENT 4

Overview: 

In this assignment, you’ll write matlab functions implementing various simple algorithms. You 

will have to deal with for-loops, while-loops, and if-then-else constructs in addition to vector data 

structures. 

1. Write a script as follows. Use colon notation to create a vector from -2π to 2π with about 

20 increments per number or 250 total. The plot sin(v) in red and using “hold on” plot 

cos(v) in blue. Add a title. (10%)

2. The reverse function for vector [1 2 5 4] returns [4 5 2 1]. Write a function reverse which 

takes one input and returns one result. It should first find the length of the input, then 

using a for loop assign the “i

th” element of the result to the n+1- i

th element of the input 

vector.(15%)

3. Bouncing numbers. This function requires a while loop around an if-then-else construct. 

The input is an integer and the output is a vector composed as follows. While the number 

is not equal 1, then if it is odd, multiply by 3 and add 1; else if it is even, divide by 2. For 

example 3 should return the vector [3 10 5 16 8 4 2 1]. You will have to use vector 

concatenation v = [v n] to build the output vector because you won’t know the length in 

advance. (15%)

4. Plotting bouncing numbers. Write a script which runs bouncing numbers from 1 to 1000, 

takes the length of each output, and plots the length of each output. Also plot the 

histogram of lengths(10%)

5. Binary Padding. Given a vector of 1’s and 0’s and a length like 16, adds 0’s to the left of 

the vector until it is the correct length. Make sure it does something reasonable with a 

input vector which is too long. (10%)

6. Decimal to Binary: write a function dec2bin which converts a decimal number to a vector 

of 1’s and 0’s/ you know that mod(n 2) returns 1 or 0 if a number is odd or even. And you 

already wrote reverse. Now its just a question of while the number is ~= 0 to keep 

dividing by 2 after saving the remainder in a list.(15%)

7. Binary to decimal. Now you have to write a for loop with a sum gathering the powers of 

2 which are selected by the 1’s in the vector. Are you going to calculate two to the 

highest power and divide by 2, or reverse the vector and start from 1 by powers of 

2?(10%)

8. Binary Addition. This function takes 2 vectors of 1’s and 0’s representing binary numbers 

of the same length (which you can get using padding), add the numbers together (without 

converting to decimal). Demonstrate with 150 Plus 90 (15%)

What to submit and how:

Submit your “.m” files individually and save your plots in a doc file and then as a pdf named 

firstlast-hw4.pdf (replace “firstlast” with your first and last name and submit via Latte

.

Due date: Sun, Mar 24 at 11:55 PM. Late policy is 5% of the assignment value per day.