Floating Point Arithmetic Operations
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Questions and Answers

What is the result of subtracting 0.7254 E5 from 0.7288 E5?

  • 0.0050 E5
  • 0.0036 E5
  • 0.0034 E5 (correct)
  • 0.0040 E5

    • When subtracting 0.7253 E2 from 0.5467 E5, what is the result?

  • 0.5470 E5
  • 0.5450 E5
  • 0.5480 E5
  • 0.5460 E5 (correct)

    • What is the result of subtracting 0.7254 E(-99) from 0.7288 E(-99)?

  • 0.0036 E(-99)
  • 0.0040 E(-99)
  • 0.0050 E(-99)
  • 0.0034 E(-99) (correct)

    • When subtracting 0.5423 E(-1) from 0.6298 E2, what is the result?

    <p>0.6293 E2</p> Signup and view all the answers

    What is the result of subtracting 0.2834 E(-99) from 0.5492 E(-97)?

    <p>0.5464 E(-97)</p> Signup and view all the answers

    What is the rule for multiplication of floating-point numbers?

    <p>Mantissa parts are multiplied and the exponents are added.</p> Signup and view all the answers

    What is the condition for adding two floating-point numbers?

    <p>The exponents must be equal</p> Signup and view all the answers

    What is the result of adding 0.3254 E5 and 0.5464 E5?

    <p>0.8718 E5</p> Signup and view all the answers

    How do you convert 0.3254 E2 to the same exponent as 0.5462 E5?

    <p>Multiply it by 10^(-3)</p> Signup and view all the answers

    What is the result of adding 0.5467 E5 and 0.7253 E3?

    <p>0.5539 E5</p> Signup and view all the answers

    What is the result of adding 0.07 E(-1) and 0.66 E(-3)?

    <p>0.7660 E(-2)</p> Signup and view all the answers

    What is the result of adding 0.7254 E2 and 0.5467 E2?

    <p>1.272 E2</p> Signup and view all the answers

    What is the condition for a decimal number to be in normalized floating point form?

    <p>The digit on the left of the decimal point should be zero, and the digit to the right of the decimal point should be non-zero.</p> Signup and view all the answers

    What is the value of x in the equation 0.0098790123 = x × 10-2?

    <p>0.98790123</p> Signup and view all the answers

    What is the truncated value of 0.0034563216789?

    <p>0.3456321 × 10-2</p> Signup and view all the answers

    What is the notation for multiplication with 10 to the power n in the normalized floating point form?

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

    What is the mantissa in the normalized floating point form?

    <p>The part before the 'E' notation</p> Signup and view all the answers

    What is the normalized floating point form of 1.2375 E5?

    <p>0.12375 E6</p> Signup and view all the answers

    Study Notes

    Floating Point Arithmetic Operations

    • Subtraction involves aligning the exponents and then performing the operation on the mantissas.
    • Example: 0.7288 E5 - 0.7254 E5 = 0.0034 E5, equivalent to 0.3400 E3.
    • Example: 0.5467 E5 - 0.7253 E2 (converted to 0.0007 E5) results in 0.5460 E5.

    Special Exponent Cases

    • When subtracting floating point numbers with negative exponents, align accordingly:
      • 0.7288 E(-99) - 0.7254 E(-99) = 0.0034 E(-99) or 0.3400 E(-101).

    Multiplication of Floating Point Numbers

    • In multiplication, the mantissas are multiplied and the exponents are added.
    • Example:
      • 0.6543 E5 x 0.2253 E3 = (0.6543 x 0.2253) E(5 + 3) = 0.1474 E8.
      • 0.1234 E5 x 0.1111 E13 = (0.1234 x 0.1111) E(5 + 13) = 0.10371 E9.
    • Standard form must be maintained post multiplication.

    Addition of Floating Point Numbers

    • Exponents must be equal for addition; select the larger one.
    • Example:
      • 0.3254 E5 + 0.5464 E5 = 0.8718 E5.
      • 0.3254 E2 converted to E5 equals 0.0003 E5, then added to 0.5462 E5 = 0.5465 E5.

    Subtraction of Floating Point Numbers

    • Similar to addition, equalize exponents before performing the operation.
    • Example:
      • 0.7254 E2 + 0.5467 E2 = 1.272 E2 or 0.1272 E3 for standard form.

    Normalization in Floating Point Representation

    • Floating point representation should have one non-zero digit to the left of the decimal point.
    • Example:
      • 0.0312 E3 becomes 0.312 E2.
      • 1.2375 E5 normalizes to 0.12375 E6.

    Truncation and Rounding

    • Operations may require truncating or rounding values to maintain precision:
      • Truncation on 0.0098790123 = 0.9879 x 10^-2.
      • Rounding 0.0034563216789 = 0.3456322 x 10^-2.

    Key Definitions

    • Mantissa: The significant part of the floating-point number (e.g., "abc" in abc E5).
    • Exponent: Indicates the power of ten by which the mantissa is multiplied (e.g., "5" in abc E5).
    • Standard Floating Point Form: mantissa and exponent structured for clarity and consistency.

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    Description

    Practice exercises for floating point arithmetic, including addition and converting numbers to standard floating point form. Covers exponent rules and notation.

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