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In this chapter you will learn what the major components of the computer are and how they work together You will also learn about the binary number system and see how it can be used to encode information at the hardware level The next two chapters will focus on programming We will first study software in general and discuss how high-level languages can be constructed to provide models in which algorithms can be expressed, and ultimately expressed in a way that the hardware can work with In the next chapter we will focus on programming using the programming language Java The goal of this chapter is not to make you an expert programmer, but instead to introduce you to the basics of programming using a language that is readily available and in wide use After learning the fundamentals of programming we will focus on operating systems, networking, and databases.

That call returns to where the second recursive call had left off at line 12. Since that is the last executable statement in the method, it also returns, back to where the first recursive call had left off at line 10. So it proceeds to line 11 with n = 3, x = 'A', y = 'B', and z = 'C'. That prints the fourth line of output:

Then line 12 executes, passing 2 to n, 'B' to x, 'A' to y, and 'C' to z. That call, HanoiTowers(2, 'B', 'A', 'C'), recursively moves the stack of two disks from peg B to to peg C via peg A and generates the last three lines of output:

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The topics covered in these chapters will address common techniques used to manage computer hardware, provide access to network resources, and manage and store data Almost every modern computer application uses the technologies discussed in these chapters The last chapter in the book will discuss some of the social issues of computing In this chapter we will discuss intellectual property rights and conflicts, privacy of data, hacking, and viruses We will also discuss our professional responsibilities when lives depend on the systems on which we work REVIEW QUESTIONS 11 Write an algorithm for your morning routine, from the time the alarm clock rings until you leave the house for work or school 12 Find or invent an algorithm to calculate the square root of any number Apply the algorithm to the number 2046, finding its square root to 2 decimal places.

Move top disk from peg B to peg A. Move top disk from peg B to peg C. Move top disk from peg A to peg C.

Since the previous four moves had already transferred the largest disk from peg A to peg C, this completes the task.

Do not use a computer or calculator! 13 Perl is a computer language that is often used for quick, one-off programming jobs, like converting text in a document from one format to another ADA is a language used for Department of Defense applications where human life may be at stake What differences would you imagine to find when you compare Perl with ADA 14 Why might a computer scientist with a primary interest in databases also need to know about networking 15 The acronym API stands for Application Programming Interface What do you suppose API means with respect to an operating system.

MUTUAL RECURSION When a function calls itself, it is called direct recursion. Another form of recursion is when a function calls other functions that call other functions that eventually call the original function. This is called indirect recursion. Its most common form is when two functions call each other. This is called mutual recursion. (See Figure 9.6.)

The sine and cosine functions from trigonometry can be defined in several different ways, and there are several different algorithms for computing their values. The simplest (although not the most efficient) is via mutual recursion. It is based upon the identities: sin2 = 2sin cos cos2 = 1 2(sin )2 and the two Taylor polynomials: sin x x x 3/6

CHAP. 1]

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public class TestMutualRecursion { public static void main(String[] args) { String fmt1 = "%18s%18s%18s%n"; String fmt2 = "%18.13f%18.13f%18.13f%n"; System.out.printf(fmt1, "s(x) ", "Math.sin(x) ", "error "); for (double x = 0.0; x < 1.0; x += 0.1) { System.out.printf(fmt2, s(x), Math.sin(x), Math.sin(x) - s(x)); } System.out.printf(fmt1, "c(x) ", "Math.cos(x) ", "error "); for (double x = 0.0; x < 1.0; x += 0.1) { System.out.printf(fmt2, c(x), Math.cos(x), c(x) - Math.cos(x)); } } public static double s(double x) { if (-0.005 < x && x < 0.005) { return x - x*x*x/6; // basis } return 2*s(x/2)*c(x/2); // recursion } public static double c(double x) { if (-0.005 < x && x < 0.005) { return 1.0 - x*x/2; // basis } return 1 - 2*s(x/2)*s(x/2); // recursion } }

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