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"**Part B: Managing Data and Memory**\n",
"\n",
"- How is data stored in memory?\n",
" - *Chapter 5*: Numbers & Bits\n",
" - *Chapter 5*: [Numbers & Bits <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)\n",
" - *Chapter 6*: Text & Bytes\n",
" - *Chapter 7*: Sequential Data\n",
" - *Chapter 8*: Map, Filter, & Reduce\n",

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"**Note**: Click on \"*Kernel*\" > \"*Restart Kernel and Clear All Outputs*\" in [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) *before* reading this notebook to reset its output. If you cannot run this file on your machine, you may want to open it [in the cloud <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_mb.png\">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/01_elements/07_resources.ipynb)."
]
},
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"cell_type": "markdown",
"metadata": {

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Chapter 5: Numbers & Bits (TL;DR)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"There exist three numeric types in core Python:\n",
"- `int`: a near-perfect model for whole numbers (i.e., $\\mathbb{Z}$); inherently precise\n",
"- `float`: the \"gold\" standard to approximate real numbers (i.e., $\\mathbb{R}$); inherently imprecise\n",
"- `complex`: layer on top of the `float` type to approximate complex numbers (i.e., $\\mathbb{C}$); inherently imprecise\n",
"\n",
"Furthermore, the [standard library <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/index.html) provides two more types that can be used as substitutes for the `float` type:\n",
"- `Decimal`: similar to `float` but allows customizing the precision; still inherently imprecise\n",
"- `Fraction`: a near-perfect model for rational numbers (i.e., $\\mathbb{Q}$); built on top of the `int` type and therefore inherently precise\n",
"\n",
"The *important* takeaways for the data science practitioner are:\n",
"\n",
"1. **Do not mix** precise and imprecise data types, and\n",
"2. actively expect `nan` results when working with `float` numbers as there are no **loud failures**.\n",
"\n",
"The **numerical tower** is Python's way of implementing various **abstract** ideas of what numbers are in mathematics."
]
}
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 5: Numbers & Bits (Review Questions)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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",
"\n",
"Be concise in your answers! Most questions can be answered in *one* sentence."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Essay Questions "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Answer the following questions briefly with *at most* 300 characters per question!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q1**: In what way is the **binary representation** of `int` objects *similar* to the **decimal system** taught in elementary school?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2**: Why may objects of type `bool` be regarded a **numeric type** as well?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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",
"\n",
"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",
"\n",
"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?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q4**: What does it mean for a code fragment to **fail silently**?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q5**: Explain why the mathematical set of all real numbers $\\mathbb{R}$ can only be **approximated** by floating-point numbers on a computer!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q6**: How do we deal with a `float` object's imprecision if we need to **check for equality**?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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 $\\text{e}$?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q8**: How can **abstract base classes**, for example, as defined in the **numerical tower**, be helpful in enabling **duck typing**?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## True / False Questions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Motivate your answer with *one short* sentence!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q13**: The following code fragment raises an `InvalidOperation` exception. That is an example of code **failing loudly**.\n",
"```python\n",
"float(\"inf\") + float(\"-inf\")\n",
"```"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q14**: Python provides a `scientific` type (e.g., `1.23e4`) that is useful mainly to model problems in the domains of physics or astrophysics."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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*."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**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*."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
}
],
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"display_name": "Python 3",
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Variables & References;
Mutability;
Expressions & Statements)
- [exercises <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/03_exercises.ipynb)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/01_elements/03_exercises.ipynb)
- [exercises <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/04_exercises.ipynb)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/01_elements/04_exercises.ipynb)
(Python as a Calculator)
- [summary <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/04_summary.ipynb)
- [review questions <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/05_review.ipynb)
- [further resources <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/06_resources.ipynb)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/01_elements/06_resources.ipynb)
- [summary <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/05_summary.ipynb)
- [review questions <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/06_review.ipynb)
- [further resources <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/01_elements/07_resources.ipynb)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/01_elements/07_resources.ipynb)
- *Chapter 2*: Functions & Modularization
- [content <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/02_functions/00_content.ipynb)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/02_functions/00_content.ipynb)
@ -112,6 +112,34 @@ Alternatively, the content can be viewed in a web browser
(Throwing Dice)
- [summary <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/04_iteration/05_summary.ipynb)
- [review questions <img height="12" style="display: inline-block" src="static/link/to_nb.png">](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/develop/04_iteration/06_review.ipynb)
- **Part B: Managing Data and Memory**
- *Chapter 5*: Numbers & Bits
- [content <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)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/05_numbers/00_content.ipynb)
(`int` Type;
Binary & Hexadecimal Representations;
Bit Arithmetic;
Bitwise Operators)
- [content <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)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/05_numbers/01_content.ipynb)
(`float` Type;
Floating-point Standard;
Special Values;
Imprecision;
Binary & Hexadecimal Representations)
- [content <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)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/05_numbers/02_content.ipynb)
(`complex` Type;
Numerical Tower;
Duck vs. Goose Typing)
- [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)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/05_numbers/03_appendix.ipynb)
(`Decimal` Type;
`Fraction` Type)
- [summary <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/04_summary.ipynb)
- [review questions <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/05_review.ipynb)
- [further resources <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/06_resources.ipynb)
[<img height="12" style="display: inline-block" src="static/link/to_mb.png">](https://mybinder.org/v2/gh/webartifex/intro-to-python/develop?urlpath=lab/tree/05_numbers/06_resources.ipynb)
#### Videos