1. Representation of data types
Integers (int) are represented as a signed binary number.
Ex. (5)10 = (0101)2
(-5)10 = (?)2
Take the 1-complement of 0101, That is 1010, and add 1 which gives is the representation of -5
The left-most bit is named the sign bit.
Normally an integer is stored in a memory ”cell” that contains 16 bits.
I.e. INT_MAX is 215 = and INT_MIN is -215 =
TDBA66, VT-03 Lecture Ch 3

2. Representation of double
real number = mantissa*2exponent
Mantissa stored in finite number of bits and its value is between 0.5 and 1.0 or between -1.0 and -0.5
Round-off error and accuracy
The minimum range of double is approximately to 1037
Check DBL_MIN and DBL_MAX in file float.h
See Appendix B in text book
TDBA66, VT-03 Lecture Ch 3

3. Finite arithmetic can fail
Cancellation error: adding values of very different magnitudes might not give the expected result (out-shift)
Another cancellation error can occur when two similar values are subtracted (loosing precision)
Arithmetic underflow and overflow: underflow when the value of an expression (in absolute value) is less than DBL_MIN overflow when a value exceeds DBL_MAX
TDBA66, VT-03 Lecture Ch 3

4. peppar:~/c/Book-Figs> cat fig3_02V2.c
/* Modification of program in Fig. 3.2
* Find implementation's ranges for positive numeric data */
#include <stdio.h>
#include <limits.h> /* definition of INT_MAX */
#include <float.h> /* definitions of DBL_MIN, DBL_MAX */
#include <math.h> /* definition of pow() */
int
main(void) {
int max_number;
printf("Range of integer values of type int: %d . . %d\n",
INT_MIN, INT_MAX);
/* Compute 2 raised to 63 and compare */
max_number = pow(2,63)-1;
printf("\n2 raised to 63 minus 1 equals %d\n", max_number);
printf("Range of positive values of type double: %e . . %e\n",
DBL_MIN, DBL_MAX);
return (0); }
TDBA66, VT-03 Lecture Ch 3

5. Note! –lm makes the mathematical library to be loaded
Compile, link and load
Note! –lm makes the mathematical library to be loaded
gcc -o fig3_02V2 fig3_02V2.c –lm
peppar:~/c/Book-Figs> ./fig3_02V2
Range of integer values of type int:
2 raised to 63 minus 1 equals
Range of positive values of type double: e e+308
peppar:~/c/Book-Figs>
Output from program fig3_02V2.c
TDBA66, VT-03 Lecture Ch 3

6. Evaluation of arithmetic expressions
Integer arithmetic
Ex.1: 7/5*5 equals 1* (division)
Ex.2: 7%5*5 equals 2*5 (reminder)
The same for variables of int type.
• Real arithmetic
Ex.3: 8.0/5.0 equals (as expected)
Mixed mode 8.0/5 also equals 1.6
TDBA66, VT-03 Lecture Ch 3

7. Mixed type assignment Ex.1: double x, y;
int tal;
y=tal/5+6; /* expression of type int */
But the value of y is stored as a double
Ex.2: tal=x*y-4; /* expression is of type double*/
But the value of tal is stored as an int (the integral part of the expression)
TDBA66, VT-03 Lecture Ch 3

8. Casting
A value of an expression can be explictly cast to another data type
Ex.3: y=(double)tal/5+6; /* prevent from integer division */
Note the difference when writing
Ex.4: y=(double)(tal/5+6);
Here expression is evaluated using integer divide and the whole expression is cast to double
TDBA66, VT-03 Lecture Ch 3

9. Figure 3.7 Using Casts to Prevent Integer Division
/* Computes a test average*/
#include <stdio.h>
int
main(void) {
int total_score, num_students;
double average;
printf("Enter sum of students' scores> ");
scanf("%d", &total_score);
printf("Enter number of students> ");
scanf("%d", &num_students);
average = (double)total_score / (double)num_students;
printf("Average score is %.2f\n", average);
return (0); }
Enter sum of students' scores> 1822
Enter number of students> 25
Average score is 72.88
TDBA66, VT-03 Lecture Ch 3

10. Priority of operators See Appendix C in text book
If the same priority the evaluation goes from left to right
Ex.1: (a+b)/c is evaluated as ((a+b)/c)
Ex.2: a+b/c is evaluated as (a+(b/c))
Ex.3: a*b/z is evaluated as ((a*b)/z)
Ex.4: y-b/x-a is evaluated as ((y-(b/x))-a)
Ex.5: (y-b)/(x-a) is eval. as ((y-b)/(x-a))
TDBA66, VT-03 Lecture Ch 3

11. Predefined math functions
See page 98 in text book
Ex. write program to simulate one toss with an ordinary die
ON THE WHITEBOARD
TDBA66, VT-03 Lecture Ch 3

12. return 0;
printf("\n\n"); }
printf("%3d", two_sum);
two_sum = die_1+ die_2;
die_2= (int) floor(rand()/(double)RAND_MAX*6.0)+1;
die_1= (int) floor(rand()/(double)RAND_MAX*6.0)+1;
putchar('\n');
if (i % 20 == 0)
for (i = 0; i < n; ++i) {
scanf("%d", &n);
"How many throws? ");
"Simulate throwing two dice a number of times.",
printf("\n%s\n%s",
srand(time(NULL)); /* nitialize the random number generator */
int i, n, die_1, die_2, two_sum; {
int main(void)
#include <time.h>
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
peppar:~/c/Ckod> cat slumpa.c
TDBA66, VT-03 Lecture Ch 3

13. Simple user-written functions
Functions without parameters (neither input nor output)
See Fig. 3.15
TDBA66, VT-03 Lecture Ch 3

14. printf("The square root of the second number is %.2f\n", second_sqrt);
second_sqrt = sqrt(second);
scanf("%lf", &second);
printf("Enter a second number> ");
/* Get second number and display its square root */
printf("The square root of the number is %.2f\n", first_sqrt);
first_sqrt = sqrt(first);
scanf("%lf", &first);
printf("Enter a number> ");
/* Get a number and display its square root. */
instruct(); /*************Call of function instruct **************/
/* Display instructions */
sum_sqrt; /* output - square root of sum */
second_sqrt, /* output - square root of second input */
first_sqrt, /* output - square root of first input value */
double first, second, /* input - two data values */ {
main(void)
int
void instruct(void); /* Displays user instructions */
#include <math.h> /* definition of sqrt */
#include <stdio.h> /* definitions of printf, scanf */
/* Performs three square root computations */
Figure Program with a User-Defined Function
TDBA66, VT-03 Lecture Ch 3

15. /* Display the square root of the sum of the two numbers. */
Fig cont.
/* Display the square root of the sum of the two numbers */
sum_sqrt = sqrt(first + second);
printf(
"The square root of the sum of the two numbers is %.2f\n",
sum_sqrt);
return (0); }
/* Displays user instructions*/
void
instruct(void) {
printf("This program demonstrates the use of the \n");
printf("math library function sqrt (square root).\n");
printf("You will be asked to enter two numbers --\n");
printf("the program will display the square root of \n");
printf("each number and the square root of their sum.\n\n");
TDBA66, VT-03 Lecture Ch 3