Question

State whether each of the following is true or false. If false, explain why. a) Java operators are evaluated from left to right. b) The following are all valid variable names: _under_bar_, m928134, t5, j7, her_sales\(, his_\)account_total, a, b$, c, z and z2. c) A valid Java arithmetic expression with no parentheses is evaluated from left to right. d) The following are all invalid variable names: 3g, 87, 67h2, h22 and 2h.

Short answer

a) True, with the caveat on operator precedence. b) False, 'her_sales(', 'his_)account_total', and 'b$' are invalid. c) False, operator precedence affects the evaluation order. d) True, all listed variable names are invalid because they start with a digit.

Step-by-step solution

Evaluating Java Operator Precedence

In Java, operators have a specific precedence that dictates how expressions are evaluated. However, operators with the same precedence level are evaluated left to right, except for assignment operators, which are evaluated right to left. The statement 'Java operators are evaluated from left to right' is generally true but incomplete without the context of operator precedence and associativity rules.

Validity of Variable Names

In Java, a valid variable name must start with a letter (A to Z or a to z), currency character (such as \(), or an underscore (_). After the first character, variable names can contain any combination of letters, digits (0 to 9), currency characters, or underscores. Among the given examples, 'her_sales(' and 'his_)account_total' are invalid because they contain parentheses, and 'b\)' is invalid due to the dollar sign not being at the beginning. All other examples are valid, assuming they don't contain other disallowed characters.

Evaluation of a Java Arithmetic Expression Without Parentheses

Java arithmetic expressions without parentheses are evaluated according to operator precedence and associativity rules. For operators of different precedences, the evaluation is not strictly left to right. For example, in the expression '2 + 3 * 4', the multiplication is performed first, despite being on the right, because it has a higher precedence than addition. Thus, this statement is false because precedence affects evaluation order, not just a left-to-right rule.

Evaluating the Validity of Given Variable Names

Variable names in Java cannot start with a digit, so '3g', '87', '67h2', 'h22', and '2h' are all invalid. Each of these examples begins with a number, which is against Java's variable naming rules.

Key concepts

Java Operator Precedence

Understanding the order in which operations are performed in a Java expression is essential. That's where Java operator precedence comes into play. In an equation, certain operations are completed before others based on a predefined hierarchy. For instance, multiplication and division have a higher precedence than addition and subtraction. This means that in the expression 2 + 3 * 4, the multiplication is carried out first, resulting in 14, not the addition, which would incorrectly yield 20. This rule helps prevent ambiguity in how an expression is evaluated and ensures consistent results across different Java programs.

To really grasp this concept, remember that operations with higher precedence are always completed first, and if there are operations with the same level of precedence, they are evaluated according to their associativity, usually from left to right. However, assignment operators are an exception, being evaluated from right to left.

Java Variable Validity

When naming variables in Java, it's crucial to follow specific rules, or else your code simply won't compile. A valid variable name must start with either a letter, an underscore (_), or a currency character like the dollar sign (\(). After the first character, you can include any combination of letters, digits (0-9), currency characters, and underscores. Hence, names like _under_bar_ and m928134 are fine because they adhere to these conventions. However, using parentheses or starting with a digit breaks these rules, rendering names like her_sales( and 3g invalid.

In regard to the exercise, it's also important to avoid special symbols like the dollar sign in the middle or end of a variable name. Doing so will lead to errors, making names like b\) incorrect. By sticking to these rules, you ensure that your variable names are always valid in Java.

Java Arithmetic Expression Evaluation

The evaluation of arithmetic expressions in Java follows the precedence and associativity rules. This means that simply reading an expression from left to right and calculating in that order doesn't always yield the correct result. Expressions without parentheses are assessed by first looking at the operator precedence. Take the expression 2 + 3 * 4, where the multiplication part 3 * 4 is performed before the addition because multiplication has a higher precedence.

When parentheses are introduced, they take the utmost precedence, altering the normal order of operations. For example, in (2 + 3) * 4, the addition within the parentheses is calculated first because parentheses effectively increase the precedence of the operations they enclose. The associativity rules only apply when operators of the same precedence appear together in an expression.

Java Operators Associativity

When we have operators of the same precedence in an expression, we then look at the associativity of operators to decide how to evaluate them. Java operators are usually left-associative, meaning they are processed from left to right. For instance, the subtraction in 10 - 5 - 2 is evaluated from left to right, thus yielding 3 as the result, not 7. One notable exception to this rule is the assignment operator, which has right-to-left associativity. So, in the expression x = y = 5, the section y = 5 is evaluated first.

Understanding associativity is vital when expressions include operators with equal precedence because it steers the order of operation execution. Clearly, comprehension of both precedence and associativity is important to parse and evaluate expressions accurately in Java, as they dictate the exact order in which the operations occur.