1. Please pick up an attendance question and submit in 5 minutes CS 1003 Lecture #3 Sept 12, 2006 Knarig Arabshian

2. Announcements Check assigned readings on the web HW1 is on the class website. –Need both lectures this week for the homework. –Due in 2 weeks. –Will be submitted electronically. Instructions posted on the class website. Post all HW questions on the web board but make sure you don’t give solutions away!

3. Agenda Binary numbers Types, operators and expressions Control Statements Loops Go over attendance question

4. Binary Numbers A computer’s internal storage techniques are different from the way people represent information in lives Information inside a digital computer is stored as a collection of binary data (0’s and 1’s) –why? Each memory location that a 0 or 1 is stored in is called a bit for binary digit A collection of 8 bits = 1 byte

5. Decimal Numbering System Base-10 There are 10 distinct single digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Do you remember this from elementary school? –Ones place –Tens place –Hundreds place –etc. Each position is a power of 10 3052 = 3 x 10 3 + 0 x 10 2 + 5 x 10 1 + 2 x 10 0

6. Binary Numbering System Base-2 There are 2 distinct digits 0, 1 Each position is a power of 2 –Ones place –Twos place –Fours place –Eights place –Sixteens place –etc. In order to get the decimal representation of a binary number you multiply 1101 = 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 Binary-to-decimal algorithm: –Whenever there is a 1 in a column, add the positional value of that column to a running sum and whenever there is a 0 in a column, add nothing Given n bits, what is the maximum number stored? –2 n – 1 Given a number n, what is the maximum number of bits needed? –Floor(log 2 n) + 1

7. Conversion Table

8. Binary Addition Is much easier to do than in decimal Rules that define arithmetic addition only needs 2 x 2 = 4 entries instead of 10 x 10 = 100 –0 + 0 = 0 –0 + 1 = 1 –1 + 0 = 1 –1 + 1 = 10 (0, with a carry of 1)

9. Binary Addition Adding the numbers 7 and 14 is as follows: 1110 00111 + 01110 ------------ 10101 carry digit

10. How about signed numbers? First bit represents the sign (+) or (-) 0 means positive, 1 means negative 1110001 - 49

11. How about signed numbers? How does the computer know if the number 1110001 represents -49 rather than the unsigned whole number 113? –Computer does not know. It depends on how the number is used –If the integer variable is declared as a signed integer, then the number 1110001 represents -49 –If the integer variable is declared as an unsigned integer then the number 1110001 represents 113 –Considering the context in which it is used is the only way to determine –Real life examples: The word ball can either be a round object used to play games or an elegant formal party Only way to know which definition it represents is to see how the word is used in a sentence

12. Some problems… What happens with the following number? 1000000 Is this 0 or -0? Will result in programs executing in different ways on different machines To avoid this problem, computer designers use two’s complement representation –Given a certain number of bits, write out every combination of 0’s and 1’s –Numbers starting with a 1 are (-), numbers starting with 0 are (+)

13. Let’s look at an example for 3 bits 000 001 010 011 100 101 110 111 (0) (-1) (-2) (-3) (-4) (+3) (+2) (+1) Given n bits, what’s the range?

14. Two’s Complement Representation Given n bits, what’s the range? –2 (n-1) to 2 (n-1) -1 –There will be one more negative number –Not ideal, but better than having two types of 0s! Try adding any two numbers in 2’s complement (3) + (-3) 011 + 101 = 000 = 0 -2 + 1 110 + 001 = 111 = -1

15. What’s the algorithm for getting two’s complement? 010  110 001  111 1001101  0110011 Take the binary number Get the 1’s complement (flip the digits) Add 1 to the result to get the 2’s complement 010  101 + 1  110 001  110 + 1  111 1001101  0110010 + 1  0110011

16. Binary Numbers Any Questions? More on binary numbers in the next class…

17. Types, operators and expressions

18. Variables Store values used during computation Conceptually similar to a mathematical variable, but need to provide more information Variables must first be declared A variable declaration announces the type of information that the variable will hold –Example: int x; char c; –x is a variable that will hold an integer value –c is a variable that will hold a character value Different types are: –int –char –float Single precision floating point –double Double precision floating point

19. Types int –short int = 16 bits –long int = 32 bits –It depends on the compiler and machine which type of integer “int” will default to. For unix it will default to long int -2 16 to 2 16 -1 ~ -2 billion to 2 billion char –A single byte, capable of holding one character in the local character set –Also a small integer char c = 5;  valid expression Can specify if a type is unsigned or signed for chars and any integer –unsigned int will have range 0 to 2 32 -1 –Why?

20. Assignment Once we’ve declared our variables, we will assign them to values –x = 5 This can also be done during declaration time –int x = 5; Make sure variables are initialized before usage!

21. Arrays We may want to store a list of variables all of the same type Instead of declaring 100’s of integer variables with different names, we can use arrays int a[100]; ... a[0] a[1] a[2] a[3] a[99] We access each element by its Index: a[0] is the 1 st element a[1] is the 2 nd element a[99] is the 100 th element The declaration: int numArray[100]; is equivalent to declaring 100 integer variables one after the other: int num1; int num2; … int num100; memory

22. Arrays Data manipulation with arrays is usually done using loops Example program: summing a list of integers main() { int n[100]; int sum, i; i = sum = 0; while (i < 100) { sum = sum + n[i] }

23. Array Assignments During declaration –int a[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} –char str[10] = {‘h‘, ‘e‘, ‘l‘, ‘l‘, ‘o‘, ‘!‘} Later on int a[10]; int i = 0; while (i < 10) { a[i] = i++; } Make sure arrays are initialized before usage!

24. Operators Mathematical operators –+, -, *, / –precedence rules apply! –x = (a + b) * (c + d) / 2 Assignment operators –=, +=, -=, ++, -- –x = 5  store value of 5 in x –x++  increase the value of x by 1 –x += 1  does the same thing –x = x + 1  and yet again the same thing –More later…

25. Constants We don’t need to declare variables for everything; we can just put numbers in place –printf(“%d”, 10+15) We can also declare variables as constants –const double PI = 3.141592654; –const char str[15] = “Hello!“; A string constant or literal –sequence of zero or more characters surrounded by double quotes: “Hello!“ –Technically it is an array of characters ending with the null character ‘\0‘ –strlen() function returns the length of a string excluding the ‘\0‘ character: strlen(str) returns 5 Hello\0! str [0] [1] [2] [3] [4] [5] [6]

26. Type Conversions Automatic conversions convert a narrower operand into a wider one without losing information –integer to floating point number f + i –char to integer c + I Conversions that will not always work –From wide to narrow long int to short int  may have loss of information

27. Type Conversions Convert strings to numeric values –int num = atoi(“1234“) –long int longNum = atol(“1234“); –double floatNum = atof(“123.4“); Convert char to int char c = ‘5‘;  represents an integer value which is a number in the machine’s character set int n = c – ‘0‘;  Subtract the ASCII value of ‘0‘ from the ASCII value of ‘5‘

28. Types Any Questions? More on types in the next class…

29. Control statements Program needs to adjust behavior based on situation –Real life example: if it is raining, take an umbrella; else if it is sunny, take sunglasses; and so on.. –Similar in programming if (expression1) statement1 else if (expression2) statement2 else statement3 Example: /* Check to see if user input is greater than 5 */ int input = 0; printf(“Please enter a number \n“); scanf(“%d”, &input); if (input > 5) printf(“Input is greater than 5\n”); else printf(“Input is not greater than 5\n”);

30. Control Statements Scope if (expr1) statement1; else statement2; if (expr2){ statement1; statement2; } else { statement3; statement4; } if (expr2){ statement1; statement2; } else { statement3; statement4; } Make sure you indent!

31. Relational and Logic Operators Relational Operators –Equals: == –Greater than: > –Less than: < –Greater than or equal to: >= –Less than or equal to: <= –Does not equal: != Logic Operators –And: && –OR: || –Not: !

32. Relational and Logic Operators Examples: –Check if an integer variable is between the numbers 1 and 5 or the numbers 10 and 15 –Check if something is valid int x = 3; if ( ((x >=1) && (x = 10) &&(x <=15)) ) printf(“In correct range \n“); int valid = 0; if (!valid) printf(“Not valid \n“);

33. Relational and Logic Operators Precedence –&& is higher than ||, but both are lower than relational and equality operators int x, y, z; x = 1; y = 13; z = 9; if (x 10) printf(“Numbers are correct\n”); else printf(“Numbers are not correct\n”); What will this print out?

34. Relational and Logic Operators Remember: “==“ is *NOT* the same as “=“ –“=“ is an assignment operator, while “==“ is a boolean test –If you make this mistake in a control statement, the condition will always be true because you are just assigning a value What will this print out? int x = 3; if (x = 5 ) printf(“x is 5!\n“); else printf(“x is not 5\n“);

35. Control Statements Any Questions? More on control statements in the next class…

36. Loops Sometimes you may need to repeat a set of statements (remember the very first algorithm you learned?) Do a set of statements until a condition is true Traverse a list and do an operation on each element Etc.

37. Loops while –Condition in parentheses is tested –If it is true, the body of the loop is executed: can be one or more statements –Then the condition is re-tested –If true, the body is executed again –When the test becomes false, the loop ends and execution continues at the statement that follows the loop –Body if it has more than one statement, it needs to be enclosed in { } if it only has one statement braces are not necessary, but correct indentation is necessary to ease readability while (i < j) i = 2 * i; while (i < j) i = 2 * i;Both work, but first one is cleaner code

38. Loops while –infinite loops happen when the condition in the while loop is always true –make sure your loop ends (unless it is meant to run infinitely…) –most common error: keeping a counter and forgetting to increment the counter (attendance question)

39. Loops Any Questions? More on loops in the next class…

40. Attendance Question #include main() { int i = 0; while (i <= 5) { printf("Hello, world!\n); }