Mathematical and Logical Operators

Understanding Operators in Sheerpower

Operators are the symbols that perform operations on variables and values. They are the building blocks for doing math, making comparisons, and creating logic in your programs. This tutorial is broken down into three parts to make learning easy and fun.

Part 1: The Basics - Mathematical Operators

These are the operators you use for basic arithmetic.

+ (Addition) - (Subtraction) * (Multiplication) / (Division) ^ (Exponentiation, e.g., 2^3 is 8) ++ (Increment, adds 1 to a variable, e.g., counter++)

Example: Calculating a Shopping Bill

apple_price = 0.50 banana_price = 0.30 num_apples = 4 num_bananas = 6 ! Calculate the cost for each fruit total_apple_cost = apple_price * num_apples total_banana_cost = banana_price * num_bananas ! Calculate the subtotal subtotal = total_apple_cost + total_banana_cost print "Subtotal: $"; subtotal ! Add one more apple num_apples++ print "Number of apples is now: "; num_apples

Part 2: Making Decisions - Relational and Logical Operators

These operators are used to compare values and combine conditions, which is essential for making decisions in your code.

Relational Operators (for comparing values)

= (Equal to) <> (Not equal to) > (Greater than) < (Less than) >= (Greater than or equal to) <= (Less than or equal to)

Logical Operators (for combining true/false conditions)

AND (Returns true if BOTH conditions are true) OR (Returns true if AT LEAST ONE condition is true) NOT (Reverses the condition, true becomes false)

Example: Qualifying for a Discount

is_member? = true purchase_total = 75.00 ! Check if the customer gets a discount is_eligible? = is_member? OR purchase_total > 100.00 print "Is eligible for discount? "; is_eligible?

Logical Operators on Numeric Values (Bitwise Operations)

When used with numeric values, these same operators perform bitwise operations. Each bit of the number is processed individually.

AND (Bitwise AND — keeps bits that are set in BOTH values) OR (Bitwise OR — keeps bits set in EITHER value) NOT (Bitwise NOT — flips all bits) XOR (Bitwise exclusive OR — keeps bits that differ)

Example: Working with Flags

// Example bit flags read_flag = 1 // 0001 write_flag = 2 // 0010 execute_flag = 4 // 0100 // Combine flags using OR permissions = read_flag OR write_flag // 0011 // Test if write flag is set has_write? = (permissions AND write_flag) <> 0 // Toggle a flag using XOR permissions = permissions XOR write_flag // removes write_flag print "Permissions: "; permissions print "Has write? "; has_write?

Bitwise vs Logical — Why It Matters

Problem: Developers often assume AND/OR always operate on true/false values, which leads to confusion when numbers are involved.

Solution: In Sheerpower, the same operators work consistently across both boolean and numeric contexts. When applied to numbers, they operate at the bit level.

Efficiency: Bitwise operations are extremely fast and allow compact representation of multiple flags inside a single numeric value.

Advanced Logical Operators

Sheerpower also supports more advanced logical operators. Their behavior is easiest to understand using "Truth Tables."

Truth Table for XOR, IMP, and EQV
X	Y	X XOR Y	X IMP Y	X EQV Y
TRUE	TRUE	FALSE	TRUE	TRUE
TRUE	FALSE	TRUE	FALSE	FALSE
FALSE	TRUE	TRUE	TRUE	FALSE
FALSE	FALSE	FALSE	TRUE	TRUE

Part 3: How It All Works - Order of Operations

Sheerpower, like all programming languages, follows a specific order when evaluating expressions. This is called operator precedence. Understanding this order is crucial for getting the correct results.

Order of Operations

Parentheses `()`
Expressions inside parentheses are always evaluated first.
Exponentiation `^`
Powers are calculated next.
Multiplication `*` and Division `/`
These are evaluated from left to right.
Addition `+` and Subtraction `-`
These are evaluated next, from left to right.
Relational & Logical Operators
Comparisons and logical operations are done last.

Example: In the expression `4 + 5 * 2`, the multiplication `5 * 2` happens first, resulting in `10`. Then the addition `4 + 10` is performed, giving a final result of `14`. To change this, you would use parentheses: `(4 + 5) * 2`, which evaluates to `18`.

For more common math functions, see Common Math Functions.

Summary: You've learned about the three main types of operators in Sheerpower: mathematical for calculations, relational and logical for decision-making, and the all-important order of operations that ensures your expressions are evaluated correctly.

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