4: Floating Point Numbers

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What type of number is represented by 'float' in programming?

Character

Integer

Boolean

Floating point (correct)

The program reads a temperature in Fahrenheit and converts it to Celsius.

False

Which two types of floating point numbers are mentioned?

float and double

In programming, a ______ variable can hold decimal values.

float Signup and view all the answers

Match the variable types with their characteristics:

float = Single precision floating point double = Double precision floating point int = Whole numbers char = Single character Signup and view all the answers

What will the variable 's' hold after the execution of the for loop in the provided code?

2 Signup and view all the answers

Local variables defined within a function retain their value after the function ends.

False Signup and view all the answers

What type of loop is used to execute a block of code repeatedly while a condition is true?

while loop Signup and view all the answers

In the given code, the keyword '_____' is used to define the start of a block of code that will execute repeatedly.

for Signup and view all the answers

Match the following terms with their descriptions:

Local Variables = Variables that are accessible only within the function they are declared in While Statement = A control structure that executes code as long as the condition is true Jump Statements = Statements that cause the program to jump to a different part of the code Do Statement = A control structure similar to a while statement that guarantees at least one execution Signup and view all the answers

What is the main difference between 'float' and 'double' data types?

Double has greater precision and requires more memory. Signup and view all the answers

The modulo operator % can be used with float data types.

False Signup and view all the answers

What will happen if zero is entered during the division input process in a for loop?

The loop will break. Signup and view all the answers

In a do-while loop, the body of the loop is guaranteed to execute at least _______.

once Signup and view all the answers

Match the following loop types to their characteristics:

while = Executes code as long as the condition is true do-while = Always executes at least once for = Iterates a specific number of times block = Defines the scope of a variable Signup and view all the answers

What is the correct way to store user input as a float variable?

std::cin >> c; Signup and view all the answers

Variables in a block have global scope until they are declared.

False Signup and view all the answers

What will be the data type of 'k' in the provided loops for division?

double Signup and view all the answers

Study Notes

Introduction to Computer Science

Course offered by the Department of Computer Science, ETH Zurich
Course code: 252-0032, 252-0047, 252-0058
Offered in Fall 2024
Authors: Manuela Fischer and Felix Friedrich

Floating Point Numbers

Discusses the float and double types and their representation as floating-point numbers on computers
Shows how to represent temperature conversions from Celsius to Fahrenheit.
Integer division rounds towards zero.
Using float type allows for fractional results.
C++ automatically converts integer values to float in mixed-type expressions.
Floating-point numbers use a fixed number of significant digits and an exponent for representing numbers.
There are different representations, some more and some less space-efficient
Floating-point numbers have a large range, sufficient for most applications.
The float type has approximately 7 digits for the mantissa and an exponent up to ±38.
The double type has even 15 digits for the mantissa and an exponent up to ±308 .
Floating-point literals can have a decimal comma and/or an exponent (scientific notation).
By default, floating-point literals have the double type.
Special floating-point values include 0, ∞, NaN, and denormalized numbers.

Fixed and Floating Point Numbers

Fixed-point numbers have a fixed number of digits before and after the decimal point, leading to a smaller range of representable values compared to floating-point numbers.
Floating-point numbers allow for more flexible representation of a broader range of numbers, but might have gaps in the possible values.
Floating-point numbers represent a number using a mantissa and an exponent, making the representation more flexible and enabling representation of a wider range of numbers.

Floating Point Numbers in C++

float and double fundamental types approximate real numbers.
Arithmetic operations on floating-point numbers are analogous to integer operations, but division is real-valued (not integer-division).
In mixed expressions, integers are converted to floating-point numbers.

Floating Point Number Systems

A floating-point number system uses parameters β (base), p (precision), emin (smallest exponent), and emax(largest exponent) to define the representation of a floating point number.
Represents numbers in the form ± do.d1...dp-1.Be where do ≠ 0.
Floating-point numbers are not contiguous; there are holes in the value range.

IEEE Standard 754

Defines floating-point number systems and their rounding behavior.
Defines single and double precision floating point types, float and double, with specific bit configurations for the mantissa, exponent, and sign.

Floating Point Rules

Avoid comparing floating-point numbers for exact equality. Use a small tolerance instead.
Avoid adding floating-point numbers with very different magnitudes, as the smaller number might get lost in the calculation.
Avoid subtracting floating-point numbers with very similar magnitudes to avoid cancellation errors.
Converting between decimal and binary representations can lead to issues, as some decimal fractions cannot be precisely represented in binary.
The order of operations in calculations involving floating point types can affect the results with different results based on the order of execution.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers the fundamentals of floating point numbers as defined in the Introduction to Computer Science course. It explores the representation of float and double types, temperature conversions, and the behavior of integer division in C++. Learn about the precision and range of floating-point representations used in computer applications.