“Operators” (i.e. “symbols”) Overview: Specific Symbols that Represent Specific Actions Arithmetic Relational Boolean Output values

Overview: most Operators There are 3 primary groups of operators One programming operator is very different from its use in math: 1. ARITHMETIC + Addition - Subtraction * Multiplication /,\ Division ^ Exponentiation, i.e. “To the power of” 2. RELATIONAL < strictly less than > strictly greater than <= less than or equal to >= greater than or equal to == is equal to ~= is not equal to 3. BOOLEAN && “AND” || “OR” ~ “NOT” = “the assignment operator”

4 * 5 -5 Overview, cont. Operators work on operands. Binary Operator Requires two operands to work 4 * 5 operands Multiplication operator -5 Unary Operator Requires one operand to work operand Negative operator

kineticEnergy = 1 / 2 * mass * vel ^ 2 Overview, cont. There are 2 types of operands: Numerical 1, 3.5, -47 Logical true, false Arithmetic (+, -, /, *, ^, =) and relational (<, <=, >, >= ,==, ~=) operators work with numerical operands Numerical Operands kineticEnergy = 1 / 2 * mass * vel ^ 2 Arithmetic operators Assign operator: “place one or more values into memory”

Overview, cont. There are 2 types of operands: Numerical 1, 3.5, -47 Logical true, false Boolean (&&,||,~) operators work on logical operands “ if this is true and this is false… do something” if (it's raining outside) and (you have an umbrella) go, you won't get wet else stay inside! end

True, False, 1, and 0?! True False 1

3. Relational Operators Relational operators allow a comparison to be evaluated. Is thrust_a greater than thrust_b?  True / False Is surface1 equal to surface2?  True / False? Is load1 less than or equal to load2?  True / False? Examples: thrust_a > thrust_b Is thrust_a strictly greater than thrust_b? radius <=0 Is radius negative or zero? nb_attempts<= 3 Is the number of attempts less than or equal to 3? 3 >= nb_attempts Is 3 greater than or equal to the number of attempts? value ~= 2 Is value not equal to 2?

Relational Operators, cont. ***COMPARISON*** == y == 5 % “Does y hold the value 5?” % “Is y equal to 5?” Example: menuChosen == 1 % did user choose menu #1 ?

Relational Operators, cont. ***COMPARISON*** == y == 5 % “Does y hold the value 5?” % “Is y equal to 5?” Example: menuChosen == 1 % did user choose menu #1 ? Assignment = % A numerical operator y = 5; % “Store the value 5 in the % variable y” Note that == and = are DIFFERENT!

Spaces or not? When one relational operator is made up of 2 symbols (<=, >=, ~=, ==): KEEP THEM GLUED TOGETHER

Spaces or not? When one relational operator is made up of 2 symbols (<=, >=, ~=, ==): KEEP THEM GLUED TOGETHER Regardless of which operator is used, a space can be used before and/or after. All these are identical to MATLAB: thrustA<=thrustB %no spaces anywhere thrustA <=thrustB %1 space before the operator thrustA<= thrustB %1 space after the operator thrustA <= thrustB %1 space before AND after

4. Boolean Operators These operators take logical scalar values and perform some operation on them to yield a logical value Two Boolean operators allow to COMBINE relational expressions && Logical AND || Logical OR One Boolean operator allows to NEGATE the result ~ Logical NOT “Negates”: turns true values into false, and false values into true

Boolean Operator #1: && “logical and” Two & symbols (“Ampersand”), glued together && Both relational expressions must be true for the combined expression to be true X && Y yields true if and only if both X and Y are true e.g. (3 < 5) && (8 >= 8) ? (x < 1) && (x > 5) ? x = 52.1; (5.5 < x) && (x < 100.2) ?

&&, continued Use of parenthesis e.g. (3<5) && (8>=8) true same as 3<5 && 8>=8 true (x<3) && (x>5) false same as x<3 && x>5 false For sanity, at least use spaces before/after the operator!

True/False What is the result of the following statement? (2 > 3) && (3 < 29.3) True False Impossible to determine (22 > 3) && (3 > 29.3) (22 > x) && (x > 29.3) True False Impossible to determine (x<2) && (y>0)

True/False In other words, there are 4 options: F && T T && F F && F

Boolean Operator #2: || “logical or” Two | (“pipe”) symbols, glued together || At least ONE relational expressions must be true for the combined expression to be true X || Y yields true if either X or Y (or both) are true e.g. (3<5) || (5>=8) ? x = 4.2; (x< 3) || (x > 5) ?

True/False What is the result of the following statement? (2 > 3) || (3 < 29.3) True False Impossible to determine (22 > 3) || (3 > 29.3) (22 > x) || (x > 29.3) True False Impossible to determine (x<2) || (y>0)

True/False Again, there are 4 options: F || T T || F F || F T || T

Priorities between Boolean Operators Which operator has priority in the following? 1 + 1 + 0 * 1 Just like * has priority over + , && has priority over || What is the result of this statement? x = 44.5; y = 55; (x<=50) || (0<y) && (y<40) ? ((x<=50) || (0<y)) && (y<40) ? (x<=50) || ((0<y) && (y<40)) ?

Boolean Operator #3: NOT One ~ symbol (“tilde”) “NOT” : negates a value Example: x = true; %keyword is known to MATLAB y = ~x; %y now has the value false The value y entered by the user should NOT be between 4 and 9 cm, inclusive: % Suppose the user enters 7.4 as a value for y ~(4<=y && y<=9) ?

5. Operators: Result values Type Operand type Result type Arithmetic: Numbers Numbers e.g. 5 * 3 15 Relational: Numbers Logical e.g. 5 < 3 false Boolean: Logical Logical e.g. ~true false true & false

Order of Operations Operator Priority Parenthesis () Highest Exponentiation ^ Unary: -, NOT ~ Multiplication/division: * / \ Addition/subtraction: + - Relational: <, <=, >, >=, ==, ~= AND: && OR: || Assignment: = Lowest