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Notes on hashing and unary/binary x86 ops.

c-declarations
Joshua Potter 2024-05-19 15:07:38 -06:00
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commit 16ffe8d4ef
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notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
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"Basic": [

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---
title: "2024-05-19"
---
- [x] Anki Flashcards
- [x] KoL
- [ ] Sheet Music (10 min.)
- [ ] Go (1 Life & Death Problem)
- [ ] Korean (Read 1 Story)
* Flashcards on x86-64 [[instructions#Unary Operations|unary operations]] and [[instructions#Binary Operations|binary operations]].

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* Exploration of the law of [[pred-trans#Distributivity of Conjunction|Distributivity of Conjunction]].
* Flashcards for left-child, right-sibling tree representations.
* Distinguish [[set/index#Classes|classes]] and sets. Discuss Zermelo-Fraenkel and von Neumann-Bernays alternatives.
* Distinguish [[set/index#Classes|classes]] and sets. Discuss Zermelo-Fraenkel and von Neumann-Bernays alternatives.
* First play test for Hide and Seek. Decided to move forward with building the mobile apps.

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---
title: "2024-05-18"
---
- [x] Anki Flashcards
- [x] KoL
- [ ] Sheet Music (10 min.)
- [ ] Go (1 Life & Death Problem)
- [ ] Korean (Read 1 Story)
* Notes on direct-address tables.
* Notes on the subset axioms and Russell's paradox.

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---
title: Direct Addressing
TARGET DECK: Obsidian::STEM
FILE TAGS: hashing::direct
tags:
- hashing
---
## Overview
Given a universe of keys $U = \{0, 1, \ldots, m - 1\}$, a **direct-address table** has $m$ **slots**. Each slot corresponds to a key in universe $U$.
%%ANKI
Basic
With respect to hashing, what does the "universe" of keys refer to?
Back: Every potential key that may be inserted into the underlying dictionary.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153757-->
END%%
%%ANKI
Basic
Given universe $U$, how many slots must a direct-address table have?
Back: $|U|$
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153762-->
END%%
%%ANKI
Basic
What name is given to each position in a direct-address table?
Back: A slot.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153766-->
END%%
%%ANKI
Basic
Given a direct-address table, the element at slot $k$ has what key?
Back: $k$.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153770-->
END%%
%%ANKI
Basic
Given a direct-address table, an element with key $k$ is placed in what slot?
Back: The $k$th slot.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153775-->
END%%
%%ANKI
Basic
Write pseudocode to test membership of $x$ in direct-address table `T[0:m-1]`.
Back
```c
bool membership(T, x) {
return T[x.key] != NIL;
}
```
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153781-->
END%%
%%ANKI
Basic
Write pseudocode to insert $x$ into direct-address table `T[0:m-1]`.
Back
```c
void insert(T, x) {
T[x.key] = x;
}
```
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153785-->
END%%
%%ANKI
Basic
Write pseudocode to delete $x$ from direct-address table `T[0:m-1]`.
Back
```c
void delete(T, x) {
T[x.key] = NIL;
}
```
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1716046153789-->
END%%
## Bibliography
* Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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---
title: Hashing
tags:
- hash
---

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@ -260,7 +260,7 @@ Given any command $S$, $$wp(S, F) = F$$
%%ANKI
Basic
Given command $S$, what does $wp(S, F)$ evaluate to?
Back: The empty set.
Back: $F$.
Reference: Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
<!--ID: 1715806256907-->
END%%

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---
title: Axioms
TARGET DECK: Obsidian::STEM
FILE TAGS: set
tags:
- set
---
## Overview
Enderton describes ten different axioms in total which serve as the foundation of our set theory.
## Extensionality
If two sets have exactly the same members, then they are equal: $$\forall A, \forall B, (x \in A \Leftrightarrow x \in B) \Rightarrow A = B$$
%%ANKI
Basic
What does the extensionality axiom state?
Back: If two sets have exactly the same members, then they are equal.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069247-->
END%%
%%ANKI
Basic
How is the extensionality axiom expressed using first-order logic?
Back: $$\forall A, \forall B, (x \in A \Leftrightarrow x \in B) \Rightarrow A = B$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734312-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall A, \forall B, (x \in A \Leftrightarrow x \in B) \Rightarrow A = B$$
Back: The extensionality axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069254-->
END%%
%%ANKI
Basic
How many sets exist with no members?
Back: Exactly one.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069256-->
END%%
%%ANKI
Basic
Which set theory axiom proves uniqueness of $\varnothing$?
Back: The extensionality axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069259-->
END%%
## Empty Set Axiom
There exists a set having no members: $$\exists B, \forall x, x \not\in B$$
%%ANKI
Basic
What does the empty set axiom state?
Back: There exists a set having no members.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734322-->
END%%
%%ANKI
Basic
How is the empty set axiom expressed using first-order logic?
Back: $$\exists B, \forall x, x \not\in B$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734327-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\exists B, \forall x, x \not\in B$$
Back: The empty set axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734332-->
END%%
%%ANKI
Basic
Which set theory axiom proves existence of $\varnothing$?
Back: The empty set axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069259-->
END%%
%%ANKI
Basic
What two properties ensures definition $\varnothing$ is well-defined?
Back: The empty set exists and is unique.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034312-->
END%%
%%ANKI
Basic
How is the empty set defined using set-builder notation?
Back: $\{x \mid x \neq x\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348141-->
END%%
## Pairing Axiom
For any sets $u$ and $v$, there exists a set having as members just $u$ and $v$: $$\forall u, \forall v, \exists B, \forall x, (x \in B \Leftrightarrow x = u \lor x = v)$$
%%ANKI
Basic
What does the pairing axiom state?
Back: For any sets $u$ and $v$, there exists a set having as members just $u$ and $v$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734337-->
END%%
%%ANKI
Basic
How is the pairing axiom expressed using first-order logic?
Back: $$\forall u, \forall v, \exists B, \forall x, (x \in B \Leftrightarrow x = u \lor x = v)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734341-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall u, \forall v, \exists B, \forall x, (x \in B \Leftrightarrow x = u \lor x = v)$$
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734346-->
END%%
%%ANKI
Basic
Which set theory axiom proves existence of set $\{x, y\}$ where $x \neq y$?
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734351-->
END%%
%%ANKI
Basic
Which set theory axiom proves existence of set $\{x\}$?
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734357-->
END%%
%%ANKI
Basic
For sets $u$ and $v$, what name is given to set $\{u, v\}$?
Back: The pair set of $u$ and $v$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034322-->
END%%
%%ANKI
Basic
In set theory, what does a singleton refer to?
Back: A set with exactly one member.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034325-->
END%%
%%ANKI
Basic
What set theory axiom is used to prove existence of singletons?
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034329-->
END%%
%%ANKI
Basic
How is the pair set $\{u, v\}$ defined using set-builder notation?
Back: $\{x \mid x = u \lor x = v\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348148-->
END%%
## Union Axiom
### Preliminary Form
For any sets $a$ and $b$, there exists a set whose members are those sets belonging either to $a$ or to $b$ (or both): $$\forall a, \forall b, \exists B, \forall x, (x \in B \Leftrightarrow x \in a \lor x \in b)$$
%%ANKI
Basic
What does the union axiom (preliminary form) state?
Back: For any sets $a$ and $b$, there exists a set whose members are all in either $a$ or $b$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034333-->
END%%
%%ANKI
Basic
How is the union axiom (preliminary form) expressed using first-order logic?
Back: $$\forall a, \forall b, \exists B, \forall x, (x \in B \Leftrightarrow x \in a \lor x \in b)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034337-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall a, \forall b, \exists B, \forall x, (x \in B \Leftrightarrow x \in a \lor x \in b)$$
Back: The union axiom (preliminary form).
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034341-->
END%%
%%ANKI
Basic
How is the union of sets $a$ and $b$ denoted?
Back: $a \cup b$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034346-->
END%%
%%ANKI
Basic
What two set theory axioms prove existence of e.g. $\{x_1, x_2, x_3\}$?
Back: The pairing axiom and union axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034351-->
END%%
%%ANKI
Basic
How is the union of set $a$ and $b$ defined using set-builder notation?
Back: $\{x \mid x \in a \lor x \in b\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348153-->
END%%
## Power Set Axiom
For any set $a$, there is a set whose members are exactly the subsets of $a$: $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
%%ANKI
Basic
What does the power set axiom state?
Back: For any set $a$, there exists a set whose members are exactly the subsets of $a$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034356-->
END%%
%%ANKI
Basic
How is the power set axiom expressed using first-order logic?
Back: $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034361-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
Back: The power set axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034368-->
END%%
%%ANKI
Basic
How is $x \subseteq a$ rewritten using first-order logic and $\in$?
Back: $\forall t, t \in x \Rightarrow t \in a$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034375-->
END%%
%%ANKI
Basic
How is the power set of set $a$ denoted?
Back: $\mathscr{P}{a}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034381-->
END%%
%%ANKI
Basic
How is the power set of set $a$ defined using set-builder notation?
Back: $\{x \mid x \subseteq a\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348160-->
END%%
## Bibliography
* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).

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---
title: Classes
TARGET DECK: Obsidian::STEM
FILE TAGS: set::class
tags:
- class
- set
---
## Overview
The **Zermelo-Fraenkel alternative** avoids speaking of collections defined using set theoretical notation that are not sets. The **von Neumann-Bernays** alternative calls these **classes**.
%%ANKI
Basic
In set theory, what is a class?
Back: A collection defined using set theoretical notation that isn't a set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576758-->
END%%
%%ANKI
Basic
Which two alternatives are usually employed when speaking of classes?
Back: The Zermelo-Fraenkel alternative and the von Neumann-Bernays alternative.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576761-->
END%%
%%ANKI
Basic
What does the Zermelo-Fraenkel alternative say about classes?
Back: It gives it no ontological status at all.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576763-->
END%%
%%ANKI
Basic
What does the von Neumann-Bernays alternative say about classes?
Back: It refers to objects defined using set theory but that aren't actually sets.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576765-->
END%%
%%ANKI
Cloze
The {1:Zermelo}-{2:Fraenkel} alternative is a separate approach from the {2:von Neumann}-{1:Bernays} alternative.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576766-->
END%%
%%ANKI
Basic
Which set theory alternative avoids the term "class"?
Back: The Zermelo-Fraenkel alternative.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576768-->
END%%
%%ANKI
Basic
Which set theory alternative embraces the term "class"?
Back: The von Neumann-Bernays alternative.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576769-->
END%%
%%ANKI
Basic
What kind of mathematical object is $\{x \mid x \neq x\}$?
Back: A set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576771-->
END%%
%%ANKI
Basic
What kind of mathematical object is $\{x \mid x = x\}$?
Back: A class.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576774-->
END%%
%%ANKI
Basic
Are sets or classes more general?
Back: Classes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576777-->
END%%
%%ANKI
Basic
Is every set a class?
Back: Yes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576779-->
END%%
%%ANKI
Basic
Is every class a set?
Back: No.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576781-->
END%%
%%ANKI
Basic
Assuming entrance requirement $\_\_\_$, what kind of mathematical object is $\{x \mid \_\_\_\}$?
Back: A class.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576782-->
END%%
## Russell's Paradox
Let $R = \{x \mid x \not\in x\}$. Then $R \in R \Leftrightarrow R \not\in R$.
%%ANKI
Basic
What simpler set is $\{x \mid x \neq x\}$ equivalent to?
Back: The empty set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576772-->
END%%
%%ANKI
Basic
Is $\{x \mid x \neq x\}$ a set?
Back: Yes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074591194-->
END%%
%%ANKI
Basic
What simpler set is $\{x \mid x = x\}$ equivalent to?
Back: N/A. This is a class.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576775-->
END%%
%%ANKI
Basic
Is $\{x \mid x = x\}$ a set?
Back: No.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074591199-->
END%%
%%ANKI
Basic
What simpler set is $\{x \mid x \in x\}$ equivalent to?
Back: The empty set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074591202-->
END%%
%%ANKI
Basic
Is $\{x \mid x \in x\}$ a set?
Back: Yes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074610694-->
END%%
%%ANKI
Basic
What simpler set is $\{x \mid x \not\in x\}$ equivalent to?
Back: N/A. This is a class.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074591205-->
END%%
%%ANKI
Basic
Is $\{x \mid x \not\in x\}$ a set?
Back: No.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074610697-->
END%%
%%ANKI
Basic
Let $R = \{x \mid x \not\in x\}$. What biconditional demonstrates a paradox?
Back: $R \in R \Leftrightarrow R \not\in R$
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743527-->
END%%
%%ANKI
Basic
Given $R = \{x \mid x \not\in x\}$, what contradiction arises when we assume $R \in R$?
Back: The entrance requirement says $R \not\in R$.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075811572-->
END%%
%%ANKI
Basic
Given $R = \{x \mid x \not\in x\}$, what contradiction arises when we assume $R \not\in R$?
Back: $R$ satisfies the entrance requirement meaning $R \in R$.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075811577-->
END%%
%%ANKI
Basic
What special name is given to class $\{x \mid x \not\in x\}$?
Back: The Russell set.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743531-->
END%%
%%ANKI
Basic
Explain how the Russell set is defined in plain English.
Back: It is the "set" of all sets that do not contain themselves.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743534-->
END%%
%%ANKI
Basic
What is the entrance requirement of the Russell set?
Back: $x \not\in x$
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743537-->
END%%
%%ANKI
Basic
The barber paradox is a variant of what other paradox?
Back: Russell's paradox.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743540-->
END%%
%%ANKI
Basic
What does the barber paradox assume existence of?
Back: A barber who shaves all those, and those only, who do not shave themselves.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743544-->
END%%
%%ANKI
Basic
What question is posed within the barber paradox?
Back: Does the barber shave himself?
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743547-->
END%%
%%ANKI
Basic
In the barber paradox, what contradiction arises when we assume the barber shaves himself?
Back: The barber *only* shaves those who do not shave themselves.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743551-->
END%%
%%ANKI
Basic
In the barber paradox, what contradiction arises when we assume the barber does not shave himself?
Back: The barber shaves *all* men who do not shave themselves.
Reference: “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
<!--ID: 1716075743555-->
END%%
## Bibliography
* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
* “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).

444
notes/set/index.md
View File

@ -134,130 +134,392 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
<!--ID: 1715786028667-->
END%%
## Classes
The **Zermelo-Fraenkel alternative** avoids speaking of collections defined using set theoretical notation that are not sets. The **von Neumann-Bernays** alternative calls these **classes**.
## Extensionality
If two sets have exactly the same members, then they are equal: $$\forall A, \forall B, (x \in A \Leftrightarrow x \in B) \Rightarrow A = B$$
%%ANKI
Basic
In set theory, what is a class?
Back: A collection defined using set theoretical notation that isn't a set.
What does the extensionality axiom state?
Back: If two sets have exactly the same members, then they are equal.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576758-->
<!--ID: 1715649069247-->
END%%
%%ANKI
Basic
Which two alternatives are usually employed when speaking of classes?
Back: The Zermelo-Fraenkel alternative and the von Neumann-Bernays alternative.
How is the extensionality axiom expressed using first-order logic?
Back: $$\forall A, \forall B, (x \in A \Leftrightarrow x \in B) \Rightarrow A = B$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576761-->
<!--ID: 1715649734312-->
END%%
%%ANKI
Basic
What does the Zermelo-Fraenkel alternative say about classes?
Back: It gives it no ontological status at all.
The following encodes which set theory axiom? $$\forall A, \forall B, (x \in A \Leftrightarrow x \in B) \Rightarrow A = B$$
Back: The extensionality axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576763-->
<!--ID: 1715649069254-->
END%%
%%ANKI
Basic
What does the von Neumann-Bernays alternative say about classes?
Back: It refers to objects defined using set theory but that aren't actually sets.
How many sets exist with no members?
Back: Exactly one.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576765-->
<!--ID: 1715649069256-->
END%%
%%ANKI
Basic
Which set theory axiom proves uniqueness of $\varnothing$?
Back: The extensionality axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069259-->
END%%
## Empty Set Axiom
There exists a set having no members: $$\exists B, \forall x, x \not\in B$$
%%ANKI
Basic
What does the empty set axiom state?
Back: There exists a set having no members.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734322-->
END%%
%%ANKI
Basic
How is the empty set axiom expressed using first-order logic?
Back: $$\exists B, \forall x, x \not\in B$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734327-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\exists B, \forall x, x \not\in B$$
Back: The empty set axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734332-->
END%%
%%ANKI
Basic
Which set theory axiom proves existence of $\varnothing$?
Back: The empty set axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649069259-->
END%%
%%ANKI
Basic
What two properties ensures definition $\varnothing$ is well-defined?
Back: The empty set exists and is unique.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034312-->
END%%
%%ANKI
Basic
How is the empty set defined using set-builder notation?
Back: $\{x \mid x \neq x\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348141-->
END%%
## Pairing Axiom
For any sets $u$ and $v$, there exists a set having as members just $u$ and $v$: $$\forall u, \forall v, \exists B, \forall x, (x \in B \Leftrightarrow x = u \lor x = v)$$
%%ANKI
Basic
What does the pairing axiom state?
Back: For any sets $u$ and $v$, there exists a set having as members just $u$ and $v$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734337-->
END%%
%%ANKI
Basic
How is the pairing axiom expressed using first-order logic?
Back: $$\forall u, \forall v, \exists B, \forall x, (x \in B \Leftrightarrow x = u \lor x = v)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734341-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall u, \forall v, \exists B, \forall x, (x \in B \Leftrightarrow x = u \lor x = v)$$
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734346-->
END%%
%%ANKI
Basic
Which set theory axiom proves existence of set $\{x, y\}$ where $x \neq y$?
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734351-->
END%%
%%ANKI
Basic
Which set theory axiom proves existence of set $\{x\}$?
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715649734357-->
END%%
%%ANKI
Basic
For sets $u$ and $v$, what name is given to set $\{u, v\}$?
Back: The pair set of $u$ and $v$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034322-->
END%%
%%ANKI
Basic
In set theory, what does a singleton refer to?
Back: A set with exactly one member.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034325-->
END%%
%%ANKI
Basic
What set theory axiom is used to prove existence of singletons?
Back: The pairing axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034329-->
END%%
%%ANKI
Basic
How is the pair set $\{u, v\}$ defined using set-builder notation?
Back: $\{x \mid x = u \lor x = v\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348148-->
END%%
## Union Axiom
### Preliminary Form
For any sets $a$ and $b$, there exists a set whose members are those sets belonging either to $a$ or to $b$ (or both): $$\forall a, \forall b, \exists B, \forall x, (x \in B \Leftrightarrow x \in a \lor x \in b)$$
%%ANKI
Basic
What does the union axiom (preliminary form) state?
Back: For any sets $a$ and $b$, there exists a set whose members are all in either $a$ or $b$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034333-->
END%%
%%ANKI
Basic
How is the union axiom (preliminary form) expressed using first-order logic?
Back: $$\forall a, \forall b, \exists B, \forall x, (x \in B \Leftrightarrow x \in a \lor x \in b)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034337-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall a, \forall b, \exists B, \forall x, (x \in B \Leftrightarrow x \in a \lor x \in b)$$
Back: The union axiom (preliminary form).
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034341-->
END%%
%%ANKI
Basic
How is the union of sets $a$ and $b$ denoted?
Back: $a \cup b$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034346-->
END%%
%%ANKI
Basic
What two set theory axioms prove existence of e.g. $\{x_1, x_2, x_3\}$?
Back: The pairing axiom and union axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034351-->
END%%
%%ANKI
Basic
How is the union of set $a$ and $b$ defined using set-builder notation?
Back: $\{x \mid x \in a \lor x \in b\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348153-->
END%%
## Power Set Axiom
For any set $a$, there is a set whose members are exactly the subsets of $a$: $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
%%ANKI
Basic
What does the power set axiom state?
Back: For any set $a$, there exists a set whose members are exactly the subsets of $a$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034356-->
END%%
%%ANKI
Basic
How is the power set axiom expressed using first-order logic?
Back: $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034361-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom? $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
Back: The power set axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034368-->
END%%
%%ANKI
Basic
How is $x \subseteq a$ rewritten using first-order logic and $\in$?
Back: $\forall t, t \in x \Rightarrow t \in a$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034375-->
END%%
%%ANKI
Basic
How is the power set of set $a$ denoted?
Back: $\mathscr{P}{a}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715688034381-->
END%%
%%ANKI
Basic
How is the power set of set $a$ defined using set-builder notation?
Back: $\{x \mid x \subseteq a\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715900348160-->
END%%
## Subset Axioms
For each formula $\_\_\_$ not containing $B$, the following is an axiom: $$\forall t_1, \cdots, \forall t_k, \forall c, \exists B, \forall x, (x \in B \Leftrightarrow x \in c \land \_\_\_)$$
%%ANKI
Basic
What do the subset axioms state?
Back: For each formula $\phi$ not containing $B$, the following is an axiom: $$\forall t_1, \cdots, \forall t_k, \forall c, \exists B, \forall x, (x \in B \Leftrightarrow x \in c \land \_\_\_)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312858-->
END%%
%%ANKI
Basic
Let $\_\_\_$ be a wff excluding $B$. How is its subset axiom stated in first-order logic?
Back: $$\forall t_1, \cdots, \forall t_k, \forall c, \exists B, \forall x, (x \in B \Leftrightarrow x \in c \land \_\_\_)$$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312864-->
END%%
%%ANKI
Basic
The following encodes which set theory axiom(s)? $$\forall t_1, \cdots, \forall t_k, \forall c, \exists B, \forall x, (x \in B \Leftrightarrow x \in c \land \_\_\_)$$
Back: The subset axioms.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312869-->
END%%
%%ANKI
Basic
Which axioms prove the existence of the union of two sets?
Back: The union axiom.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312873-->
END%%
%%ANKI
Basic
Which axioms prove the existence of the intersection of two sets?
Back: The subset axioms.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312876-->
END%%
%%ANKI
Basic
How is the intersection of sets $A$ and $B$ denoted?
Back: $A \cap B$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312880-->
END%%
%%ANKI
Basic
How is the intersection of sets $a$ and $b$ defined using set-builder notation?
Back: $\{x \mid x \in a \land x \in b\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312884-->
END%%
%%ANKI
Basic
Which axioms prove the existence of the relative complement of two sets?
Back: The subset axioms.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312888-->
END%%
%%ANKI
Basic
Given sets $A$ and $B$, what does $A - B$ denote?
Back: The relative complement of $B$ in $A$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312893-->
END%%
%%ANKI
Basic
How is the relative complement of set $B$ in $A$ denoted?
Back: $A - B$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312897-->
END%%
%%ANKI
Basic
How is the relative complement of set $b$ in $a$ defined using set-builder notation?
Back: $\{x \mid x \in a \land x \not\in b\}$
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1716074312901-->
END%%
%%ANKI
Cloze
The {1:Zermelo}-{2:Fraenkel} alternative is a separate approach from the {2:von Neumann}-{1:Bernays} alternative.
Union is to the {union axiom} whereas intersection is to the {subset axioms}.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576766-->
<!--ID: 1716074312905-->
END%%
%%ANKI
Basic
Which set theory alternative avoids the term "class"?
Back: The Zermelo-Fraenkel alternative.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576768-->
END%%
%%ANKI
Basic
Which set theory alternative embraces the term "class"?
Back: The von Neumann-Bernays alternative.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576769-->
END%%
%%ANKI
Basic
What kind of mathematical object is $\{x \mid x \neq x\}$?
Back: A set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576771-->
END%%
%%ANKI
Basic
What name is given to $\{x \mid x \neq x\}$?
Back: The empty set.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576772-->
END%%
%%ANKI
Basic
What kind of mathematical object is $\{x \mid x = x\}$?
Back: A class.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576774-->
END%%
%%ANKI
Basic
What name is given to $\{x \mid x = x\}$?
Back: The class of all sets.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576775-->
END%%
%%ANKI
Basic
Are sets or classes more general?
The subset axioms ensure we do not construct what kind of mathematical object?
Back: Classes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576777-->
END%%
%%ANKI
Basic
Is every set a class?
Back: Yes.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576779-->
END%%
%%ANKI
Basic
Is every class a set?
Back: No.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576781-->
END%%
%%ANKI
Basic
Assuming entrance requirement $\_\_\_$, what kind of mathematical object is $\{x \mid \_\_\_\}$?
Back: A class.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1715970576782-->
<!--ID: 1716074312909-->
END%%
## Bibliography
* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
* “Russell’s Paradox,” in *Wikipedia*, April 18, 2024, [https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437](https://en.wikipedia.org/w/index.php?title=Russell%27s_paradox&oldid=1219576437).
* Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

4
notes/set/trees.md
View File

@ -786,7 +786,7 @@ struct Node {
struct Node *children[k];
};
```
Back: A $k$-ary child representation.
Back: A $k$-child representation.
Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
Tags: c17
<!--ID: 1715969047054-->
@ -845,7 +845,7 @@ END%%
Basic
The following is a portion of what kind of tree representation?
![[binary-tree-nodes.png]]
Back: A $k$-ary (binary) child representation.
Back: A $k$-child (binary) representation.
Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1715969525820-->
END%%

308
notes/x86-64/instructions.md
View File

@ -294,25 +294,16 @@ END%%
The MOV instruction class has four primary variants: `movb`, `movw`, `movl`, and `movq`. There also exist zero extension and sign extension variations in the forms of MOVS and MOVZ.
| Instruction | Operands | Effect | Description |
| ----------- | -------- | ---------------- | ------------------------------------------- |
| `movb` | S, D | D <- S | Move byte |
| `movw` | S, D | D <- S | Move word |
| `movl` | S, D | D <- S | Move double word |
| `movq` | S, D | D <- S | Move quad word |
| `movabsq` | I, R | R <- I | Move quad word |
| `movzbw` | S, R | R <- ZE(S) | Move zero-extended byte to word |
| `movzbl` | S, R | R <- ZE(S) | Move zero-extended byte to double word |
| `movzwl` | S, R | R <- ZE(S) | Move zero-extended word to double word |
| `movzbq` | S, R | R <- ZE(S) | Move zero-extended byte to quad word |
| `movzwq` | S, R | R <- ZE(S) | Move zero-extended word to quad word |
| `movsbw` | S, R | R <- SE(S) | Move sign-extended byte to word |
| `movsbl` | S, R | R <- SE(S) | Move sign-extended byte to double word |
| `movswl` | S, R | R <- SE(S) | Move sign-extended word to double word |
| `movsbq` | S, R | R <- SE(S) | Move sign-extended byte to quad word |
| `movswq` | S, R | R <- SE(S) | Move sign-extended word to quad word |
| `movslq` | S, R | R <- SE(S) | Move sign-extended double word to quad word |
| `cltq` | | %rax <- SE(%eax) | Sign-extend `%eax` to `%rax` |
| Instruction | Operands | Effect | Description |
| ------------ | -------- | ---------------- | ------------------------------------ |
| `mov[bwlq]` | S, D | D <- S | Move byte/word/double word/quad word |
| `movabsq` | I, R | R <- I | Move quad word |
| `movzb[wlq]` | S, R | R <- ZE(S) | Move zero-extended byte |
| `movzw[lq]` | S, R | R <- ZE(S) | Move zero-extended word |
| `movsb[wlq]` | S, R | R <- SE(S) | Move sign-extended byte |
| `movsw[lq]` | S, R | R <- SE(S) | Move sign-extended word |
| `movslq` | S, R | R <- SE(S) | Move sign-extended double word |
| `cltq` | | %rax <- SE(%eax) | Sign-extend `%eax` to `%rax` |
Notice there is no `movzlq` instruction. `movl` covers this functionality since, by convention, instructions moving double words into a 64-bit register automatically zeroes out the upper 32 bits.
@ -757,7 +748,7 @@ END%%
%%ANKI
Basic
Besides effect memory computations, how else is `leaq` used?
Besides effective memory computations, how else is `leaq` used?
Back: For certain arithmetic operations.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1715780601469-->
@ -765,7 +756,7 @@ END%%
%%ANKI
Basic
Assume `%rbx` holds $p$ and `%rdx` holds $q$. What is the value of `%rax` in the following?
Assume `%rdx` holds $q$. What is the value of `%rax` in the following?
```asm
leaq 9(%rdx),%rax
```
@ -787,7 +778,7 @@ END%%
%%ANKI
Basic
Assume `%rbx` holds $p$ and `%rdx` holds $q$. What is the value of `%rax` in the following?
Assume `%rbx` holds $p$. What is the value of `%rax` in the following?
```asm
leaq 2(%rbx, %rbx, 7),%rax
```
@ -798,7 +789,7 @@ END%%
%%ANKI
Basic
Assume `%rbx` holds $p$ and `%rdx` holds $q$. What is the value of `%rax` in the following?
Assume `%rdx` holds $q$. What is the value of `%rax` in the following?
```asm
leaq 0xE(, %rdx, 3),%rax
```
@ -807,6 +798,277 @@ Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Program
<!--ID: 1715781031941-->
END%%
### Unary Operations
| Instruction | Operands | Effect | Description |
| ----------- | -------- | ---------- | ------------ |
| `inc[bwlq]` | D | D <- D + 1 | Increment |
| `dec[bwlq]` | D | D <- D - 1 | Decrement |
| `neg[bwlq]` | D | D <- -D | Negate |
| `not[bwlq]` | D | D <- ~D | Complement |
%%ANKI
Basic
What four variants do `INC` instructions take on in x86-64?
Back: `incb`, `incw`, `incl`, `incq`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986895-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D + 1$?
Back: `INC`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743477-->
END%%
%%ANKI
Basic
What combination of source and destination types is prohibited in unary instructions?
Back: A source and destination memory address.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986904-->
END%%
%%ANKI
Basic
What do the instructions in the `INC` instruction class do?
Back: Increments the specified destination by $1$.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986907-->
END%%
%%ANKI
Cloze
The {`INC`} instruction class is to x86-64 whereas the {`++`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716126147793-->
END%%
%%ANKI
Basic
What do the instructions in the `DEC` instruction class do?
Back: Decrements the specified destination by $1$.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986910-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D - 1$?
Back: `DEC`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743483-->
END%%
%%ANKI
Cloze
The {`DEC`} instruction class is to x86-64 whereas the {`--`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716126147798-->
END%%
%%ANKI
Basic
What do the instructions in the `NEG` instruction class do?
Back: Negates the specified destination.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986913-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow -D$?
Back: `NEG`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743486-->
END%%
%%ANKI
Cloze
The {`NEG`} instruction class is to x86-64 whereas the {`-`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716126147801-->
END%%
%%ANKI
Basic
What do the instructions in the `NOT` instruction class do?
Back: Complements the specified destination.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986916-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow \textasciitilde D$?
Back: `NOT`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743488-->
END%%
%%ANKI
Cloze
The {`NOT`} instruction class is to x86-64 whereas the {`~`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716126147804-->
END%%
%%ANKI
Basic
What distinguishes the `NEG` and `NOT` instruction classes?
Back: The former negates, the latter complements.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716125986919-->
END%%
### Binary Operations
| Instruction | Operands | Effect | Description |
| ------------ | -------- | ----------- | -------------- |
| `add[bwlq]` | S, D | D <- D + S | Addition |
| `sub[bwlq]` | S, D | D <- D - S | Subtraction |
| `imul[bwlq]` | S, D | D <- D * S | Multiplication |
| `xor[bwlq]` | S, D | D <- D ^ S | Exclusive-or |
| `or[bwlq]` | S, D | D <- D \| S | Or |
| `and[bwlq]` | S, D | D <- D & S | And |
%%ANKI
Basic
What four variants do `ADD` instructions take on in x86-64?
Back: `addb`, `addw`, `addl`, `addq`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743491-->
END%%
%%ANKI
Basic
What combination of source and destination types is prohibited in `ADD` instructions?
Back: A source and destination memory address.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743494-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D + S$?
Back: `ADD`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743497-->
END%%
%%ANKI
Cloze
The {`ADD`} instruction class is to x86-64 as the {`+=`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716128138030-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D - S$?
Back: `SUB`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743500-->
END%%
%%ANKI
Basic
Which `SUB` instruction is equivalent to `decq %rcx`?
Back:
```asm
subq $1, %rcx
```
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127853102-->
END%%
%%ANKI
Basic
How does Bryant et al. recommend reading `SUB` instructions?
Back: As subtracting the first operand *from* the second.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127853106-->
END%%
%%ANKI
Cloze
The {`SUB`} instruction class is to x86-64 as the {`-=`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716128138033-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D * S$?
Back: `IMUL`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743502-->
END%%
%%ANKI
Cloze
The {`IMUL`} instruction class is to x86-64 as the {`*=`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716128138036-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D \;^\wedge\; S$?
Back: `XOR`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743505-->
END%%
%%ANKI
Cloze
The {`XOR`} instruction class is to x86-64 as the {`^=`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716128138040-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D \mid S$?
Back: `OR`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743508-->
END%%
%%ANKI
Cloze
The {`OR`} instruction class is to x86-64 as the {`|=`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716128138043-->
END%%
%%ANKI
Basic
Which instruction class corresponds to effect $D \leftarrow D \;\&\; S$?
Back: `AND`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1716127743511-->
END%%
%%ANKI
Cloze
The {`AND`} instruction class is to x86-64 as the {`&=`} operator is to C.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
<!--ID: 1716128138046-->
END%%
## Bibliography
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.