Chapter 5: Numbers & Bits (Review Questions)¶

The questions below assume that you have read the first , second , and the third part of Chapter 5. Some questions regard the Appendix ; that is indicated with a *****.

Be concise in your answers! Most questions can be answered in one sentence.

Essay Questions¶

Answer the following questions briefly with at most 300 characters per question!

Q1: In what way is the binary representation of int objects similar to the decimal system taught in elementary school?

< your answer >

Q2: Why may objects of type bool be regarded a numeric type as well?

< your answer >

Q3: Colors are commonly expressed in the hexadecimal system in websites (cf., the HTML and CSS formats).

For example, $#000000$, $#ff9900$, and $#ffffff$ turn out to be black, orange, and white. The six digits are read in pairs of two from left to right, and the three pairs correspond to the proportions of red, green, and blue mixed together. They reach from $0_{16} = 0_{10}$ for $0$% to $\text{ff}_{16} = 255_{10}$ for $100$% (cf., this article for an in-depth discussion).

In percent, what are the proportions of red, green, and blue that make up orange? Calculate the three percentages separately! How many bytes are needed to encode a color? How many bits are that?

< your answer >

Q4: What does it mean for a code fragment to fail silently?

< your answer >

Q5: Explain why the mathematical set of all real numbers $\mathbb{R}$ can only be approximated by floating-point numbers on a computer!

< your answer >

Q6: How do we deal with a float object's imprecision if we need to check for equality?

< your answer >

Q7: What data type, built-in or from the standard library , is best suited to represent the transcendental numbers $\pi$ and $\text{e}$?

< your answer >

Q8: How can abstract base classes, for example, as defined in the numerical tower, be helpful in enabling duck typing?

< your answer >

True / False Questions¶

Motivate your answer with one short sentence!

Q9: The precision of int objects depends on how we choose to represent them in memory. For example, using a hexadecimal representation gives us $16^8$ digits whereas with a binary representation an int object can have at most $2^8$ digits.

< your answer >

Q10: With the built-in round() function, we obtain a precise representation for any float object if we can live with less than $15$ digits of precision.

< your answer >

Q11: As most currencies operate with $2$ or $3$ decimals (e.g., EUR $9.99$), the float type's limitation of at most $15$ digits is not a problem in practice.

< your answer >

Q12: The IEEE 754 standard's special values provide no benefit in practice as we could always use a sentinel value (i.e., a "dummy"). For example, instead of nan, we can always use 0 to indicate a missing value.

< your answer >

Q13: The following code fragment raises an InvalidOperation exception. That is an example of code failing loudly.

float("inf") + float("-inf")

< your answer >

Q14: Python provides a scientific type (e.g., 1.23e4) that is useful mainly to model problems in the domains of physics or astrophysics.

< your answer >

Q15: From a practitioner's point of view, the built-in format() function does the same as the built-in round() function.

< your answer >

**Q16**: The Decimal type from the decimal module in the standard library allows us to model the set of the real numbers $\mathbb{R}$ precisely*.

< your answer >

**Q17**: The Fraction type from the fractions module in the standard library allows us to model the set of the rational numbers $\mathbb{Q}$ precisely*.

< your answer >