Add video and streamline content
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6e68175252
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3 changed files with 419 additions and 687 deletions
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"metadata": {},
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"source": [
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"\n",
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"# Chapter 5: Bits & Numbers"
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"# Chapter 5: Numbers & Bits"
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]
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},
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{
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@ -19,7 +19,9 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Read [Chapter 5](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/05_numbers_00_lecture.ipynb) of the book. Then, work through the questions below."
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"The questions below assume that you have read [Chapter 5](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/05_numbers_00_lecture.ipynb) in the book.\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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@ -47,7 +49,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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" < your answer >"
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]
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},
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{
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@ -61,28 +63,14 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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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**: Why is it *inefficient* to store `bool` objects in bits resembling a **hexadecimal representation**?"
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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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" "
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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**: Colors are commonly expressed in the **hexadecimal system** in websites (cf., the [HTML](https://en.wikipedia.org/wiki/HTML) and [CSS](https://en.wikipedia.org/wiki/Cascading_Style_Sheets) formats).\n",
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"**Q3**: Colors are commonly expressed in the **hexadecimal system** in websites (cf., the [HTML](https://en.wikipedia.org/wiki/HTML) and [CSS](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](https://en.wikipedia.org/wiki/RGB_color_model) for an in-depth discussion).\n",
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"\n",
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@ -93,77 +81,77 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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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**: What does it mean for a code fragment to **fail silently**?"
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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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" "
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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**: 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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"**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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" "
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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**: How do we deal with a `float` object's imprecision if we need to **check for equality**?"
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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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" "
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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**: What data type, built-in or from the [standard library](https://docs.python.org/3/library/index.html), is best suited to represent the [transcendental numbers](https://en.wikipedia.org/wiki/Transcendental_number) $\\pi$ and $\\text{e}$?"
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"**Q7**: What data type, built-in or from the [standard library](https://docs.python.org/3/library/index.html), is best suited to represent the [transcendental numbers](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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" "
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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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"**Q9**: How can **abstract base classes**, for example, as defined in the **numerical tower**, be helpful in enabling **duck typing**?"
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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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" "
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" < your answer >"
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]
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},
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{
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@ -184,63 +172,63 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**Q10**: 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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"**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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" "
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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**: With the built-in [round()](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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"**Q10**: With the built-in [round()](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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" "
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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**: 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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"**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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" "
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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 [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard's **special values** provide no benefit in practice as we could always use a **[sentinel](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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"**Q12**: The [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard's **special values** provide no benefit in practice as we could always use a **[sentinel](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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" "
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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**: The following code fragment raises an `InvalidOperation` exception. That is an example of code **failing loudly**.\n",
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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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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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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**: 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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"**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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" "
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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**: From a practitioner's point of view, the built-in [format()](https://docs.python.org/3/library/functions.html#format) function does the *same* as the built-in [round()](https://docs.python.org/3/library/functions.html#round) function."
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"**Q15**: From a practitioner's point of view, the built-in [format()](https://docs.python.org/3/library/functions.html#format) function does the *same* as the built-in [round()](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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" "
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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 `Decimal` type from the [decimal](https://docs.python.org/3/library/decimal.html) module in the [standard library](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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"**Q16**: The `Decimal` type from the [decimal](https://docs.python.org/3/library/decimal.html) module in the [standard library](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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" "
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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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"**Q18**: The `Fraction` type from the [fractions](https://docs.python.org/3/library/fractions.html) module in the [standard library](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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"**Q17**: The `Fraction` type from the [fractions](https://docs.python.org/3/library/fractions.html) module in the [standard library](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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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" "
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" < your answer >"
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]
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}
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],
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