Fundamentals of Computer Arithmetic and Errors Quiz
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Questions and Answers

What is the consequence of not all numbers being able to be represented exactly in a computer?

  • The computer crashes
  • The computer slows down
  • Numbers become larger
  • Arithmetic mistakes occur (correct)

    • How is the information in a single-precision PC built?

  • Vectors of 64 bits
  • Vectors of 128 bits
  • Vectors of 32 bits (correct)
  • Vectors of 16 bits

    • What is the representation of real numbers in a computer called?

  • Integer point
  • Fixed point
  • Rational point
  • Floating point (correct)

    • What limited bits are assigned for in the representation of real numbers in a computer?

    <p>Exponent and mantissa</p> Signup and view all the answers

    In which base are the real numbers represented in a computer?

    <p>Base 2</p> Signup and view all the answers

    What situation may occur when working with a PC, where 1+ϵ=1 and ϵ ̸= 0?

    <p>Inexact arithmetic</p> Signup and view all the answers

    In a 64-bit architecture, how many bits are dedicated to the mantissa?

    <p>52 bits</p> Signup and view all the answers

    What is the machine precision in a 64-bit setting?

    <p>$2.2 \times 10^{-16}$</p> Signup and view all the answers

    What situation arises when a representable number is smaller than the smallest representable number?

    <p>Underflow resulting in a 0 value</p> Signup and view all the answers

    What type of error can be measured by computing the difference between the approximation and the actual value?

    <p>Absolute error</p> Signup and view all the answers

    In the context of computer arithmetic, which situation refers to small changes in data leading to large changes in the solution?

    <p>Ill-conditioning</p> Signup and view all the answers

    What is the largest representable number in a 64-bit architecture?

    <p>$1.79 \times 10^{308}$</p> Signup and view all the answers

    What does the machine precision imply about the significance of digits beyond the 16th digit?

    <p>$2.2 \times 10^{-16}$</p> Signup and view all the answers

    What results from an overflow in floating point arithmetic?

    <p>$\infty$ value</p> Signup and view all the answers

    Which concept refers to the situation where rounding errors are not just propagated, but also amplified by an algorithm?

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

    What does it mean if a problem is described as ill-conditioned?

    <p>Small changes generate large changes in the solution.</p> Signup and view all the answers

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