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1 Simple Data Types Integer Types (whole numbers) Type Range Short unsigned short int unsigned int long unsigned long -32767 0 -2147483647 0 -2147483647 0 to to to to to to Data Bits 32767 65535 2147483647 4294967295 2147483647 4294967295 16 16 32 32 32 32 Floating-Point Types (real numbers) Type Range float double long double 3.4e-38 to 3.4e+38 1.7e-308 to 1.7e+308 3.4e-4932 to 3.4e+4932 Significant Digits Data Bits 6 15 19 32 64 80 Representational Error (round-off error) When representing real numbers as integers. When using real numbers with more than the available significant digits. When using real number fractions that are not exact base-2 fractions. Cancellation error When adding or subtracting large and small real numbers. This invalidates the part of the sum or difference that is smaller than the least significant digit of the larger number. Can be a very serious problem with numerical integration or trigonometric functions of angles near 0 or 90 degrees. 2 Example This code will print: a = 100000000, b = 2, c = 100000000, c-a = 0 x = 100000000, y = 2, z = 100000002, z-x = 2. #include<stdio.h> void main() { float a = 1e8, b = 2, c; double x = 1e8, y = 2, z; c = a + b; z = x + y; printf(“\n a = %0.0f, b = %0.0f, c = %0.0f,” “ c-a = %0.0f”, a, b ,c , c-a); printf(“\n x = %0.0lf, y = %0.0lf, z = %0.0lf,” “ z-x = %0.0lf”, x, y ,z , z-x); } Overflow error When the magnitude of a floating-point number is greater than allowed. Magnitude > 3.4e+38 Magnitude > 1.7e+308 Magnitude > 3.4e+4932 for type float. for type double. for type long double Causes a run-time error. Underflow error When the non-zero magnitude of floating-point number is smaller than allowed. 0 < magnitude < 3.4e-38 for type float. 0 < magnitude < 1.7e-308 for type double. 0 < magnitude < 3.4e-4932 for type long double. Causes a run-time warning. 3 Automatic Conversion of Data Types Binary operations automatically convert the less detailed numerical data type to the more detailed data type. An assignment statement automatically converts the numerical data on the right side to the numerical data type on the left side. Most library function calls automatically convert the less detailed numerical data in the argument to the more detailed data type needed by the function. Example When int k; float c; double x, y; then k/c becomes a 6-digit float type. k/x becomes a 15-digit double type. c/x becomes a 15-digit double type. k = 10/3.0; stores 3 in k. c = 10/3.0; stores 3.33333 in c. y = 10/3.0; stores 3.33333333333333 in y. sin(k) converts k to the double type needed by sin. sin(c) converts c to the double type needed by sin. 4 Explicit Data Type Conversion (Type Casting ) To cast (interpret) the data in a constant or variable as a new data type, precede the constant or the variable name by the new data type in parentheses. The data type of the constant or variable is not changed. Form (type)var where type var cons or (type)cons is a data type. is a variable name. is a constant value. Example The following code printed: int double float aa = 999999910 aa = 999999910 aa = 999999936 #include<stdio.h> void main() { int aa = 999999910; printf(“\n int aa = %d”, aa); printf(“\n double aa = %9.0lf”, (double)aa); printf(“\n float aa = %9.0f”, (float)aa ); } 5 Character Representation Character constants and variables are represented by 16-bit integers. Type Range char unsigned char -32768 0 to to 32767 65535 Collating Sequence The assignment of integers to represent characters is called a collating sequence. The ASCII collating sequence is shown in Appendix A. In the ASCII collating sequence: The numbers The letters The letters 0 to 9 A to Z a to z are assigned integers are assigned integers are assigned integers 48 to 57. 65 to 90. 97 to 122. Use a type cast to find: The collating sequence integer assigned to a given character. The character assigned to a given collating sequence integer. Example This code uses type casts to print: The ASCII code for the letter b is 98 ASCII code 75 represents the letter K #include<stdio.h> void main() { printf(“\n The ASCII code for the letter %c" " is %d”, 'b', (int)'b'); printf(“\n ASCII code %d represents” “ the letter %c", 75, (char)75); }