327 lines
10 KiB
Text
327 lines
10 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Chapter 5: Numbers & Bits (Review Questions)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The questions below assume that you have read the [first <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/05_numbers/00_content.ipynb), [second <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/05_numbers/01_content.ipynb), and the [third <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/05_numbers/02_content.ipynb) part of Chapter 5. Some questions regard the [Appendix <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_nb.png\">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/05_numbers/03_appendix.ipynb); that is indicated with a **\\***.\n",
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"\n",
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"Be concise in your answers! Most questions can be answered in *one* sentence."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Essay Questions "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Answer the following questions briefly with *at most* 300 characters per question!"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q1**: In what way is the **binary representation** of `int` objects *similar* to the **decimal system** taught in elementary school?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q2**: Why may objects of type `bool` be regarded a **numeric type** as well?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q3**: Colors are commonly expressed in the **hexadecimal system** in websites (cf., the [HTML <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/HTML) and [CSS <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Cascading_Style_Sheets) formats).\n",
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"\n",
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"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 <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/RGB_color_model) for an in-depth discussion).\n",
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"\n",
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"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?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q4**: What does it mean for a code fragment to **fail silently**?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q5**: Explain why the mathematical set of all real numbers $\\mathbb{R}$ can only be **approximated** by floating-point numbers on a computer!"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q6**: How do we deal with a `float` object's imprecision if we need to **check for equality**?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q7**: What data type, built-in or from the [standard library <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/index.html), is best suited to represent the [transcendental numbers <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Transcendental_number) $\\pi$ and $\\text{e}$?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q8**: How can **abstract base classes**, for example, as defined in the **numerical tower**, be helpful in enabling **duck typing**?"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## True / False Questions"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Motivate your answer with *one short* sentence!"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q10**: With the built-in [round() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#round) function, we obtain a *precise* representation for any `float` object if we can live with *less than* $15$ digits of precision."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q12**: The [IEEE 754 <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/IEEE_754) standard's **special values** provide no benefit in practice as we could always use a **[sentinel <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Sentinel_value)** value (i.e., a \"dummy\"). For example, instead of `nan`, we can always use `0` to indicate a *missing* value."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q13**: The following code fragment raises an `InvalidOperation` exception. That is an example of code **failing loudly**.\n",
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"```python\n",
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"float(\"inf\") + float(\"-inf\")\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q14**: Python provides a `scientific` type (e.g., `1.23e4`) that is useful mainly to model problems in the domains of physics or astrophysics."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q15**: From a practitioner's point of view, the built-in [format() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#format) function does the *same* as the built-in [round() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#round) function."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q16\\***: The `Decimal` type from the [decimal <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/decimal.html) module in the [standard library <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/index.html) allows us to model the set of the real numbers $\\mathbb{R}$ *precisely*."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q17\\***: The `Fraction` type from the [fractions <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/fractions.html) module in the [standard library <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/index.html) allows us to model the set of the rational numbers $\\mathbb{Q}$ *precisely*."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" < your answer >"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.6"
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},
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"toc": {
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"base_numbering": 1,
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"nav_menu": {},
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"number_sections": false,
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"sideBar": true,
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"skip_h1_title": true,
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"title_cell": "Table of Contents",
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"title_sidebar": "Contents",
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"toc_cell": false,
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"toc_position": {},
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"toc_section_display": false,
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"toc_window_display": false
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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