Types and Arithmetic Operators

1. Types and Arithmetic Operators CSIS 1595: Fundamentals of Programming and Problem Solving 1

2. Data Types • Each variable has specific type • numeric types (int and float) • strings • boolean (True or False) • Define capabilities of variable • Numeric types manipulated with arithmetic operators • Strings manipulated with string functions • Booleans used in branching statements

3. Dynamic Data Typing • Based on current value stored in variable x = 3  xis an integer x = “Fred”  xis now a string • Other languages (C, Java, etc.) require type to be set when variable declared and not later changed • Good idea to not change type in middle of program (confusing!) • Can use type function to see current type of variable

4. Numeric Data Types • Two different numeric types • integer (whole numbers) • floating point (numbers with decimals) • Based on type of literal assigned to variable • No decimal  integer • Decimal  float • Even if 0 after decimal 2.0is float

5. Numeric Data Types and Memory • Numeric values must be stored in binary memory • No limit to size of integers in Python • Other languages may limit to fixed storage size(64 bits, etc.) • Problem: Some numbers may require infinite number of digits to store • Example: 1/3 = 0.3333333333333333333333… • Cannot store with complete accuracy on computer!

6. Float Type and Memory • Python allocates limited number of digits for floats • Usually about 16 digits • 1/3 = 0.3333333333333333 in Python • Affects accuracy of computation • 5 * 2/3 ≠ 2/3 * 5 • Difference between integer and float numbers • integer arithmetic guaranteed to be accurate • float arithmetic not guaranteed

7. Floats and Exponential Notation • Exponential notation: digits e exponent • Equivalent to digits × 10exponent • Used to store arbitrarily large/small floats with limited number of digits • 0.0000000000000000000000000000123  1.23e-30 • Why called “floating point” numbers

8. Arithmetic Operators • Basic mathematical operators: + addition - subtraction Also have unary minus -number * multiplication / division ** exponentiation // quotient (like division but truncates result to integer) % remainder (what is left over after quotient) Example: x =23 // 5  4y = 23 % 5  3

9. Arithmetic Operators and Types • Result type based on operand type • integer op integer  integer • float op float float • float op integer or integer op float float • Exception: division • integer / integer float • Even if the operands are divisible! • If need to get a whole number, use // instead

10. Explicit Type Conversion • Can use type(value) to evaluate value as type x = float(3)  3.0 y = int(3.52)  3 • Used to manually truncate to integer • Not same as rounding! • Can convert strings to/from equivalent numbers s = str(3.52)  ‘3.52’ x = float(“3.52”)  3.52 y = int(“3”)  3

11. Parsing Input to Strings • input function always returns a string • Even if user inputs a number • Must convert to number before manipulating with arithmetic operators • Otherwise get runtime error • Usual form: • Prompt for value (stored in string) • Use int or floatto get correspond numeric value • Manipulate numeric value

12. Example: Celsius to Fahrenheit

13. Order of Evaluation • x = 7 + 3 * 2 • Is this 20? Is this 13? • Depends on order of evaluationof operators • Rules of operator precedence: • Exponentiation done first • Unary minus done next • Multiplicative operators (*, /, %, //) done next • Additive operators (+, -) done last • Operators at same level done left to right

14. Parentheses and Precedence • Can use parentheses to change order • Expression in parentheses evaluated before use in rest of expression x = (7 + 3) * 2 20

15. Incremental Operators • Many statements of form variable = variable op value • Variable changed in terms of current value • Shortcut syntax: variableop= value • Examples: x += 1 same as x = x + 1 x *= 2 same as x = x * 2 …