Decimal to Binary Conversion
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Questions and Answers

What is the primary reason why decimal numbers need to be converted to binary?

  • Humans can only understand decimal numbers
  • Binary numbers are easier to read
  • Computers only understand binary language (correct)
  • Decimal numbers are too complex

    • What is the first step in converting a decimal number to binary?

  • Divide the decimal number by 2 (correct)
  • Multiply the decimal number by 2
  • Add 1 to the decimal number
  • Subtract 1 from the decimal number

    • What is the purpose of taking the remainder and dividing it by 2 again in the decimal to binary conversion process?

  • To multiply the decimal number by 2
  • To find the square root of the decimal number
  • To find the decimal equivalent of the binary number
  • To repeat the process until the result is 0 (correct)

    • What is the final step in converting a decimal number to binary using the division method?

    <p>Read the binary digits from bottom to top</p> Signup and view all the answers

    What is the purpose of using a binary conversion table?

    <p>To convert decimal numbers to binary quickly</p> Signup and view all the answers

    What is the process of creating tiny computers and components less than 100 nanometers in size?

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

    What is the function of the Bus Interface Unit?

    <p>Allows the core to communicate with other CPU components</p> Signup and view all the answers

    What is the term for the series of operations involved in the execution of a single machine level instruction?

    <p>Machine Cycle</p> Signup and view all the answers

    What is the term for computers that use light to perform digital computations?

    <p>Optical Computing</p> Signup and view all the answers

    What is the term for the ability to process one trillion floating-point operations per second?

    <p>Tera-Scale Computing</p> Signup and view all the answers

    Study Notes

    Decimal to Binary Conversion

    Why Convert Decimal to Binary?

    • Computers only understand binary language (0s and 1s)
    • Decimal numbers are used by humans, but computers need binary to process information

    Steps to Convert Decimal to Binary

    1. Divide the decimal number by 2
      • If the result is a whole number, write down 0
      • If the result is a decimal, write down 1
    2. Take the remainder and divide it by 2 again
      • Repeat step 1 until the result is 0
    3. Read the binary digits from bottom to top
      • The resulting sequence of 0s and 1s is the binary equivalent of the decimal number

    Examples

    • Convert 12 to binary:
      • 12 ÷ 2 = 6 (0)
      • 6 ÷ 2 = 3 (0)
      • 3 ÷ 2 = 1.5 (1)
      • 1 ÷ 2 = 0.5 (1)
      • Binary equivalent: 1100
    • Convert 25 to binary:
      • 25 ÷ 2 = 12.5 (1)
      • 12 ÷ 2 = 6 (0)
      • 6 ÷ 2 = 3 (0)
      • 3 ÷ 2 = 1.5 (1)
      • 1 ÷ 2 = 0.5 (1)
      • Binary equivalent: 11001

    Shortcut: Using a Binary Conversion Table

    • Create a table with powers of 2 (2^0, 2^1, 2^2, ...)
    • Find the decimal number in the table and write down the corresponding binary digits
    • Combine the binary digits to get the binary equivalent of the decimal number

    Why Convert Decimal to Binary?

    • Computers only understand binary language, consisting of 0s and 1s
    • Decimal numbers are used by humans, but computers need binary to process information

    Steps to Convert Decimal to Binary

    • Divide the decimal number by 2, and write down 0 if the result is a whole number, or 1 if the result is a decimal
    • Take the remainder and divide it by 2 again, repeating step 1 until the result is 0
    • Read the binary digits from bottom to top to get the binary equivalent of the decimal number

    Examples of Decimal to Binary Conversion

    • 12 in decimal is equal to 1100 in binary
    • 25 in decimal is equal to 11001 in binary

    Shortcut: Using a Binary Conversion Table

    • Create a table with powers of 2 (2^0, 2^1, 2^2,...)
    • Find the decimal number in the table and write down the corresponding binary digits
    • Combine the binary digits to get the binary equivalent of the decimal number

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    Description

    Learn how to convert decimal numbers to binary language that computers understand. Understand the steps involved in the conversion process.

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