2: Integer Arithmetic and its Limits

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Questions and Answers

What is the primary purpose of the program `fahrenheit.cpp`?

To convert temperatures from Celsius to Fahrenheit (correct)

To display temperatures in Celsius

To convert temperatures from Fahrenheit to Celsius

To convert temperatures from Celsius to Kelvin

The rules of precedence and associativity in programming are unrelated to those in mathematics.

False

What is an expression in the context of a computer program?

A combination of variables, constants, and operators that computes a value.

In the provided program, the output of the Fahrenheit temperature is represented by _____.

fahrenheit Signup and view all the answers

Match the following programming terms with their definitions:

Expression = A piece of code that computes a value Precedence = The order in which operations are performed Associativity = The direction of operation evaluation Variable = A storage location identified by a name Signup and view all the answers

What type of input does the program expect to convert?

Celsius Signup and view all the answers

C++ is the programming language used in the `fahrenheit.cpp` program.

True Signup and view all the answers

What is the result of the expression 'r = a * a' in the given example?

a^2 Signup and view all the answers

The operator '*' is used for addition in arithmetic expressions.

False Signup and view all the answers

What variable is used to store the result of multiplying 'a' by itself in the provided example?

r Signup and view all the answers

In C++, the type used for positive integers without sign is called ______.

unsigned int Signup and view all the answers

Match each arithmetic operator with its function:

<ul> <li>= Multiplication / = Division</li> </ul> <ul> <li>= Addition</li> </ul> <ul> <li>= Subtraction</li> </ul> Signup and view all the answers

What does the term 'unsigned int' refer to?

A type for natural numbers, including zero Signup and view all the answers

The use of unsigned integers is always recommended in programming.

False Signup and view all the answers

What is the literal used when declaring an unsigned integer in C++?

u Signup and view all the answers

The directive advises to avoid ______ integers unless there is a specific reason for their use.

unsigned Signup and view all the answers

Match the C++ statement with its output purpose:

unsigned int a = 4; = Concurrency of int to unsigned int unsigned int b = 4u; = No conversion needed std::cout = Output data to console unsigned int c = -1; = Error due to negative value Signup and view all the answers

Study Notes

Introduction to Computer Science Course Information

Course code: 252-0032, 252-0047, 252-0058
Authors: Manuela Fischer and Felix Friedrich
Department: Computer Science, ETH Zurich
Semester: Fall 2024

Integers and Expressions (Section 3)

Computer programs use statements containing expressions
Expression rules for evaluation are similar to mathematical rules
Expression evaluation follows precedence, associativity, and arity rules
Parentheses can be used to override default evaluation order
Expression trees depict the evaluation order
Unsigned integers can have their own specific evaluation rules.

Arithmetic Expressions (Section 3.1)

Example code (fahrenheit.cpp) converts Celsius to Fahrenheit
Code includes input, computation, and output
Program demonstrates mathematical expression evaluation in C++.
Arithmetic expressions evaluate in a specific order adhering to precedence rules.

Precedence and Associativity (Section 3.2)

Multiplication/division have higher precedence than addition/subtraction
Expressions with the same precedence are evaluated from left to right
Parentheses override precedence and associativity rules
Arithmetic operators have specific precedence and associativity rules which impact the order of evaluation of operations.

Expression Trees and Evaluation Order (Section 3.3)

Expression trees visually represent the order of evaluation, with each operator node evaluating after its child nodes
Evaluation order is not uniquely determined by the expression tree structure
Avoid modifying variables within an expression more than once.
Understanding expression trees is helpful for analyzing and predicting the order operations will be executed.

Arithmetic Operators (Section 3.4)

C++ has well-defined precedence and associativity rules for arithmetic operators
Assignment operator (=) is right associative (example: a = b = c becomes a = (b=c)
Unary operators (+, −) have higher precedence than binary operators (+, -, *, /, %)
Expressions involving integer division (/) give the quotient without the remainder; a modulo operation (%) can get the remainder.

Domains and Conversions (Section 3.6)

Numbers in C++ have limited ranges
Using mixed expressions (integer + unsigned integer) can result in unexpected outputs
Use unsigned integers only when necessary
Integer literals can be declared as unsigned using a "u" suffix (e.g., 17u)
C++ guarantees that B ≥ 16 for integers
When combining signed and unsigned integers unexpected results may occur within arithmetic operations, necessitating explicit conversions when appropriate.

Signed Number Representation (Section 3.7)

Two's complement representation is the standard for representing signed integers in computers.
It handles positive and negative values efficiently.
Arithmetic operations in computers use modulo m, where m = 2^b.
Binary bit values are evaluated in order of most to least significant bits.
Understanding two's complement representation is essential for understanding how signed integers are handled in computer systems.

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Description

This quiz covers Section 3 of the Introduction to Computer Science course, focusing on integers, expressions, and the evaluation of arithmetic expressions. It discusses expression rules, precedence, associativity, and includes a practical C++ example for converting Celsius to Fahrenheit. Dive into the intricacies of expression trees and their evaluation order.