Understanding Floating Point Numbers in Decimal and Binary Systems

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the binary equivalent of 60.75 in decimal?

  • 101010.0102
  • 111100.1012 (correct)
  • 110100.112
  • 100110.1112

Using the subtraction method, what is the binary equivalent of 18.625 in decimal?

  • 10011.1102
  • 10010.1012 (correct)
  • 10110.1012
  • 11000.0112

What is the binary equivalent of 190.5625 in decimal?

  • 11100011.0112
  • 10100110.00112
  • 10011011.1102
  • 11011110.10012 (correct)

Using the multiplication and subtraction method, what is the binary equivalent of 37.25 in decimal?

<p>100101.012 (B)</p> Signup and view all the answers

What steps should be followed to convert a decimal number to binary using the subtraction method?

<p>Start with the column values, subtract from left to right, insert 0 if value cannot be subtracted or 1 if it can be, continue until the fraction becomes zero. (C)</p> Signup and view all the answers

What do input devices do?

<p>Convert data into a form that the system unit can process (A)</p> Signup and view all the answers

Which hardware devices are examples of input devices?

<p>Keyboards and mice (B)</p> Signup and view all the answers

What is the process of sampling an image called?

<p>Scanning (C)</p> Signup and view all the answers

How is an image stored using binary representation?

<p>By measuring the intensity values of distinct points located at regular intervals (D)</p> Signup and view all the answers

What does the sampling process of an image involve?

<p>Measuring the intensity values of distinct points located at regular intervals (B)</p> Signup and view all the answers

What is the color depth for an image with 256 available colors?

<p>16 bits per pixel (C)</p> Signup and view all the answers

In a black and white image, how are the pixels represented in binary?

<p>0 for white pixels and 1 for black pixels (C)</p> Signup and view all the answers

What does a higher resolution indicate about an image?

<p>More tightly packed pixels (D)</p> Signup and view all the answers

How many pixels are used to represent an image with a resolution of 300 pixels per inch?

<p>300 pixels squared (A)</p> Signup and view all the answers

What is the difference between a low resolution and a high resolution image?

<p>Low resolution images have less accurate representation (C)</p> Signup and view all the answers

Flashcards

Color depth

It represents the number of distinct colors that a pixel can have.

Input

The process of converting data, like text or images, into a form that the computer can understand.

Sampling

It involves measuring the intensity of distinct points within the image at regular intervals.

Decimal to Binary Conversion (Subtraction)

The subtraction method for converting decimal numbers to binary involves repeated subtraction of the largest power of 2 that is less than or equal to the remaining decimal value. If the subtraction is possible, you write a '1' in the corresponding binary position; otherwise, write a '0'. This process continues until the fraction becomes zero.

Signup and view all the flashcards

Image Resolution

An image's resolution refers to the density of pixels within a given area. A higher resolution signifies more pixels, resulting in a clearer and more detailed image.

Signup and view all the flashcards

Decimal to Binary Conversion (Multiplication)

The process of converting a decimal number to binary using the multiplication method involves multiplying the fractional part of the decimal number by 2 repeatedly. Every time the result is greater than or equal to 1, you write a '1' in the corresponding binary position; otherwise, write a '0'. You continue this process until the fractional part becomes zero or the desired accuracy is achieved.

Signup and view all the flashcards

Input Devices

Input devices enable us to communicate with computer systems by converting data into a format that the computer can process. They are essential for interacting with the system and providing data for computations or tasks.

Signup and view all the flashcards

System Unit

A device that interprets and executes the instructions provided by a computer user. It is responsible for processing data, controlling the flow of information, and performing operations based on the instructions received.

Signup and view all the flashcards

Input Device Examples

Keyboards and mice are common examples of input devices because they allow us to input data into the computer. Keyboards enable us to type text or control the computer's actions, while mice are used for navigating the user interface and selecting objects.

Signup and view all the flashcards

Binary Representation of an Image

Digital images are stored as a collection of pixels with individual intensity values, ranging from 0 to 255, represented in binary. Each pixel's value corresponds to its brightness level, ranging from 0 (black) to 255 (white).

Signup and view all the flashcards

Sampling an Image

The intensity values of individual pixels in an image are measured at regular intervals during the sampling process. This process determines the image's resolution and the amount of detail captured.

Signup and view all the flashcards

Black and White Image Representation

A black and white image represents each pixel's color using a single binary digit – 0 for white and 1 for black. This simplified representation allows for storing and processing images with minimal data.

Signup and view all the flashcards

High Resolution Image

A higher resolution in an image means that the pixels are more tightly packed, resulting in a more accurate and detailed representation of the image. Higher resolutions enable a clearer and more vivid display of the image's details.

Signup and view all the flashcards

Number of Pixels in an Image

The number of pixels used to represent an image is determined by its resolution. For example, an image with a resolution of 300 pixels per inch would have 300 x 300 pixels.

Signup and view all the flashcards

Low Resolution Image

A low-resolution image has fewer pixels per unit area, resulting in a less accurate and less detailed representation. This can result in blurry edges and a less crisp appearance.

Signup and view all the flashcards

Study Notes

Floating Point Numbers

  • A decimal point separates whole numbers from the fractional part in the decimal system.
  • Example: In 37.25, the whole part is 37 and the fractional part is 25/100.

Analysis of a Floating Point Number

  • The number 37.25 can be represented through digit analysis:
    • 3 in the tens place: (3 \times 10)
    • 7 in the units place: (7 \times 1)
    • 2 in the tenths place: (2 \times \frac{1}{10})
    • 5 in the hundredths place: (5 \times \frac{1}{100})
  • This representation aggregates to (37.25 = (3 \times 10) + (7 \times 1) + (2 \times \frac{1}{10}) + (5 \times \frac{1}{100})).

Binary Representation of Floating Point Numbers

  • The binary equivalent is calculated by converting whole and fractional parts separately.
  • For the whole part, methods include subtraction or division.
  • For the fractional part, use either subtraction or multiplication.

Fractional Part - Multiplication Method

  • Column values in binary representation are structured as: …, (2^5), (2^4), (2^3), (2^2), (2^1), (2^0); and fractional parts as (2^{-1}), (2^{-2}), (2^{-3}), etc.
  • Each power corresponds to specific fractional values (e.g., (1/2), (1/4), (1/8), …).

Example of Conversion using the Multiplication Method

  • To find the binary equivalent of 0.25:
    • Multiply the fraction by 2 until reaching 0:
      • (0.25 \times 2 = 0.5)
      • (0.5 \times 2 = 1.0)
    • Collect whole parts: the process yields (0.01) as the binary representation, where "1" appears after the binary point.

Summary of Conversion

  • Collect the whole parts in the order they appear after the radix point in binary representation.
  • The methodologies provided effectively convert both whole and fractional parts into binary equivalents.

Studying That Suits You

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

Quiz Team

More Like This

Use Quizgecko on...
Browser
Browser