Question

Write equivalent compound statements if possible. a. \(\quad x=2 * x\) b. \(x=x+y-2\) c. \(\quad\) sum \(=\) sum \(+\) num d. \(\quad z=z * x+2 * z\) e. \(y=y /(x+5)\)

Short answer

a. \(x *= 2\); b. unchanged; c. sum += num; d. \(z *= (x + 2)\); e. \(y /= (x + 5)\).

Step-by-step solution

Simplify Statement a

The statement given is \( x = 2 \times x \). This equation implies that the variable \( x \) is being assigned a value that is twice its original value. This operation can be simplified to the compound statement \( x *= 2 \), which multiplies the value of \( x \) by 2 and assigns it back to \( x \).

Simplify Statement b

The statement given is \( x = x + y - 2 \). This operation combines addition and subtraction with \( x \). As there is no single direct operation that combines these actions, the statement remains the same as \( x = x + y - 2 \), indicating sequential operations.

Simplify Statement c

The statement given is \( \text{sum} = \text{sum} + \text{num} \). This can be simplified to the compound statement \( \text{sum} += \text{num} \), which adds the value of \( \text{num} \) to \( \text{sum} \) and assigns the result back to \( \text{sum} \).

Simplify Statement d

The statement given is \( z = z \times x + 2 \times z \). We can factor \( z \) from both terms, leading to \( z = z (x + 2) \), and this can further be simplified using a compound statement as \( z *= (x + 2) \), which multiplies \( z \) by the sum \( x + 2 \).

Simplify Statement e

The statement is \( y = y / (x + 5) \). It reallocates the value of \( y \) to \( y \) divided by the expression \( (x + 5) \). This can be represented as the compound assignment \( y /= (x + 5) \), which divides \( y \) by \( x + 5 \) and assigns it back to \( y \).

Key concepts

Compound Statements

In programming, compound statements allow you to perform arithmetic operations on variables and immediately store the result back in the same variable. These statements are more concise than writing out the full operation. For example, in C++, the statement \(x = x - 3\) can be simplified using the compound operator to \(x -= 3\). This approach simplifies the code and makes it easier to read for anyone reviewing it later. Compound statements leverage operators like "+=", "-=", "*=", and "/=", allowing programmers to efficiently manage arithmetic operations and assignments simultaneously.
Learners should note that these compound assignments alter the original value of the variable directly. Thus, it is crucial to understand the flow of your operations when using them, as they can significantly impact the program's logic.

Variable Assignment

Variable assignment in C++ involves storing a value in a variable, making it available for future operations. When you assign a variable, say \(a = 10\), it links the variable \(a\) to the value \(10\). This assignment remains until \(a\) is reassigned a new value.
Assignments are often a part of initializing variables. They act as a temporary container for values that change as your program runs. Whenever you see a statement \(x = expr\) in C++, you know that the expression on the right is evaluated first, and its result is assigned to the variable on the left.
This is a fundamental concept in programming that allows variables to act as dynamic holders, capable of holding different values at different stages of program execution.

Arithmetic Operations

Arithmetic operations in C++ involve the basic functions of addition, subtraction, multiplication, and division. These operations are crucial as they allow for calculations and manipulations of numerical data.
The primary operators include:

• Addition (+): Adds two operands. e.g., \( a + b \).
• Subtraction (-): Subtracts the second operand from the first. e.g., \( a - b \).
• Multiplication (*): Multiplies two operands. e.g., \( a * b \).
• Division (/): Divides the first operand by the second. e.g., \( a / b \).

Understanding these operators is essential for facilitating all kinds of calculations in programming. They form the backbone of logical processing within any software system.
It is important for learners to watch the type of data they are operating on as type mismatches can generate errors or unintended results.

Expression Simplification

Expression simplification in C++ aims to reduce complex statements to more manageable forms without altering their meaning. By simplifying an expression, we improve code readability and efficiency.
For instance, consider \(z = z \times x + 2 \times z\). This can be simplified by factoring \(z\) out of the expression to yield \(z = z (x + 2)\) and efficiently rewritten as \(z *= (x + 2)\). This simplified expression is not only concise but also optimized for execution.
Expression simplification makes your code cleaner and helps prevent errors. Simplification usually involves combining like terms or leveraging arithmetic properties such as distributive, associative, or commutative rules. The goal is to maintain the original logical operation while presenting the code in a more straightforward manner.