Program Logic Formulation Meeting 6

Arithmetic Operators

• Addition, a fundamental arithmetic operation, is represented by the + (plus sign) symbol. This operator allows us to combine two or more values to obtain their total sum. In programming, this operation is often used to calculate totals such as summing up scores or computing total expenses.
• Subtraction is represented by the - (minus sign) symbol. This operator is utilized to determine the difference between two values. It’s commonly employed in situations where a deduction is necessary, such as calculating the remaining quantity after some have been taken away or determining the amount owed after payments have been made.
• Multiplication is represented by the * (asterisk) symbol, a key operator for scaling values. This operation allows for repeated addition of a quantity a specified number of times, serving essential functions in scenarios like calculating area (length multiplied by width) or determining total costs based on unit price.
• Division is represented by the / (slash) symbol. This operator divides one value by another. Division is useful in various contexts, such as distributing total amounts evenly or determining rates and averages. It's important to note how division behaves with different data types, especially in programming, as seen in integer and floating-point divisions.
• Finally, the Modulus operator is represented by % (percent), which provides the remainder of a division operation. This operator is particularly useful in situations where one needs to know if a number is even or odd, or to perform cycles or handle wrapping around in circular arrangements like time and indexes.

Rules of Precedence

• The order of operations is a critical concept that dictates the sequence in which different operations in a mathematical expression are to be evaluated. This ensures consistent outcomes across various calculations and programming environments.
• Parentheses play a vital role in providing clarity in order of operations, as they are evaluated first; if there are nested parentheses, the innermost ones are prioritized for evaluation. This enables programmers and mathematicians to control the grouping of operations effectively.
• Subsequent to evaluating within parentheses, multiplication and division operations are handled next, processed sequentially from left to right. This rule ensures that these operations are executed before addition and subtraction, which maintains the integrity of mathematical calculations.
• Following multiplication and division, addition and subtraction operations are processed from left to right. This systematic approach facilitates accurate computation and prevents ambiguity in expressions, making calculations predictable and manageable.
• A helpful mnemonic to remember the order of operations is BEDMAS, which stands for Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. This acronym serves as a guide to remember the ranking of operations while performing calculations.
• Operators with identical precedence are evaluated through a process known as left-to-right associativity. This means that in cases where the same type of operators appears in an expression, the evaluation proceeds from the leftmost operator to the right.
• The assignment operator (=), which assigns values to variables, possesses the lowest precedence of all operators in expressions. Its evaluation follows last, and it works with right-to-left associativity, meaning that in cases of multiple assignments, the rightmost operation is performed first.

Summary of Precedence and Associativity

• Operator: Assignment; Precedence: Lowest; Associativity: Right-to-Left. This implies that when multiple assignment operations are performed in one expression, the assignments are evaluated starting from the right side.
• Operator: Addition; Precedence: Medium; Associativity: Left-to-Right. Thus, if multiple addition operations are encountered, they are computed in the order they appear from left to right.
• Operator: Subtraction; Precedence: Medium; Associativity: Left-to-Right. Similar to addition, subtraction operations are evaluated in the order they are listed from left to right.
• Operator: Multiplication; Precedence: Highest; Associativity: Left-to-Right. Multiplication has priority, meaning any multiplication operations are performed first,

Arithmetic Operators

• Addition is represented by + (plus sign)
• Subtraction is represented by - (minus sign)
• Multiplication is represented by * (asterisk)
• Division is represented by / (slash)
• Modulus is represented by % (percent)

Rules of Precedence

• Order of operations determines how expressions are evaluated.
• Parentheses are evaluated first; innermost parentheses are prioritized.
• After parentheses, multiplication and division are processed from left to right.
• Addition and subtraction follow multiplication and division, also from left to right.
• Remember BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
• Identical precedence operators use left-to-right associativity.
• The assignment operator (=) has the lowest precedence, with right-to-left associativity.

Summary of Precedence and Associativity

• Operator: Assignment; Precedence: Lowest; Associativity: Right-to-Left
• Operator: Addition; Precedence: Medium; Associativity: Left-to-Right
• Operator: Subtraction; Precedence: Medium; Associativity: Left-to-Right
• Operator: Multiplication; Precedence: Highest; Associativity: Left-to-Right
• Operator: Division; Precedence: Highest; Associativity: Left-to-Right
• Operator: Modulus; Precedence: Highest; Associativity: Left-to-Right

Combinations of Assignment and Arithmetic Operators

• age += 14 is equivalent to age = age + 14
• age -= 14 is equivalent to age = age - 14
• age *= 14 is equivalent to age = age * 14
• age /= 14 is equivalent to age = age / 14
• age %= 14 is equivalent to age = age % 14

Effects of Data Type on Arithmetic Operations

• Integer and floating-point combinations work properly in addition, subtraction, multiplication, and division.
• In some programming languages, like Java, C#, and C++, integer division truncates the quotient when both numerator and denominator are integers.
• Example: int 5 / int 3 results in 1 (decimal part truncated).

Illustrations

• Expression: A = A - B + A * C / D
• Variables: If A = 5, B = 2, C = 3, and D = A, calculate the new assigned value of A.