16 Questions
What is the consequence of not all numbers being able to be represented exactly in a computer?
Arithmetic mistakes occur
How is the information in a single-precision PC built?
Vectors of 32 bits
What is the representation of real numbers in a computer called?
Floating point
What limited bits are assigned for in the representation of real numbers in a computer?
Exponent and mantissa
In which base are the real numbers represented in a computer?
Base 2
What situation may occur when working with a PC, where 1+ϵ=1 and ϵ ̸= 0?
Inexact arithmetic
In a 64-bit architecture, how many bits are dedicated to the mantissa?
52 bits
What is the machine precision in a 64-bit setting?
$2.2 \times 10^{-16}$
What situation arises when a representable number is smaller than the smallest representable number?
Underflow resulting in a 0 value
What type of error can be measured by computing the difference between the approximation and the actual value?
Absolute error
In the context of computer arithmetic, which situation refers to small changes in data leading to large changes in the solution?
Ill-conditioning
What is the largest representable number in a 64-bit architecture?
$1.79 \times 10^{308}$
What does the machine precision imply about the significance of digits beyond the 16th digit?
$2.2 \times 10^{-16}$
What results from an overflow in floating point arithmetic?
$\infty$ value
Which concept refers to the situation where rounding errors are not just propagated, but also amplified by an algorithm?
Instability
What does it mean if a problem is described as ill-conditioned?
Small changes generate large changes in the solution.
Test your knowledge on the fundamentals of computer arithmetic, errors, and how numbers are represented in computers. Understand the motivations behind studying computational mathematics and the challenges of instability and ill-conditioning in mathematical calculations.
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