Understanding Floating Point Numbers in Decimal and Binary Systems
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Understanding Floating Point Numbers in Decimal and Binary Systems

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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</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.</p> Signup and view all the answers

    What do input devices do?

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

    Which hardware devices are examples of input devices?

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

    What is the process of sampling an image called?

    <p>Scanning</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</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</p> Signup and view all the answers

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

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

    What does a higher resolution indicate about an image?

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

    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.

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    Quiz Team

    Description

    Learn about how floating point numbers are represented in the decimal system with examples, and their binary equivalence. This quiz covers the basics of floating point numbers and their analysis in both decimal and binary systems.

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