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Preliminary notes on Boolean algebra.

c-declarations
Joshua Potter 2024-02-12 14:42:11 -07:00
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notes/_journal/2024-02-12.md
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@ -11,4 +11,5 @@ title: "2024-02-12"
- [ ] Log Work Hours (Max 3 hours)
* Read 삼 년 고개 (Three-Years Hill).
* Notes on ASCII and C-style strings.
* Notes on ASCII and C-style strings.
* Elaborated on each of the submodules in Gus and my "Soft Skills Workshop".

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---
title: Boolean Algebra
TARGET DECK: Obsidian::STEM
FILE TAGS: logic::boolean
tags:
- logic
- boolean
---
## Overview
**Boolean algebra** refers to an algebraic system characterised by a set of axioms. This is something I'll explore further, probably after reading more on abstract algebra. The basic operations of Boolean algebra are negation ($\neg$), conjunction ($\land$), and disjunction ($\lor$).
%%ANKI
Basic
What C bit-level operator corresponds to $\neg$?
Back: `~`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068116-->
END%%
%%ANKI
Basic
What C bit-level operator corresponds to $\land$?
Back: `&`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068124-->
END%%
%%ANKI
Basic
What C bit-level operator corresponds to $\lor$?
Back: `|`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068132-->
END%%
%%ANKI
Basic
What C bit-level operator corresponds to $\oplus$?
Back: `^`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068137-->
END%%
%%ANKI
Basic
What is the value of `~0b00001111`?
Back: `0b11110000`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068142-->
END%%
%%ANKI
Basic
What is the value of `0b00001111 & 0b11111111`?
Back: `0b00001111`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068151-->
END%%
%%ANKI
Basic
What is the value of `0b00001111 | 0b11111111?
Back: `0b11111111`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068161-->
END%%
%%ANKI
Basic
What is the value of `0b00001111 ^ 0b11111111`?
Back: `0b11110000`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c
<!--ID: 1707774068167-->
END%%
%%ANKI
Basic
How do bit vectors represent finite sets?
Back: A `1` bit-value indicates membership at the given index.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary
<!--ID: 1707774068173-->
END%%
%%ANKI
Basic
What C bit-level operator corresponds to set complement?
Back: `~`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c set
<!--ID: 1707774068179-->
END%%
%%ANKI
Basic
What C bit-level operator corresponds to $\cup$?
Back: `|`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c set
<!--ID: 1707774068186-->
END%%
%%ANKI
Basic
What C bit-level operator corresponds to $\cap$?
Back: `&`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: binary c set
<!--ID: 1707774068192-->
END%%
%%ANKI
Basic
What is a bit mask?
Back: A bit pattern that selects certain bits of a data type.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1707774068217-->
END%%
%%ANKI
Basic
What hexadecimal bit mask returns the least significant byte of a word?
Back: `0xFF`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1707774068225-->
END%%
%%ANKI
Basic
What portable expression yields a mask of all ones, regardless of data type?
Back: `~0`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1707774068229-->
END%%
%%ANKI
Basic
Why might you prefer `~0` over e.g. `0xFFFFFFFF`?
Back: The former is independent of data type.
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1707774068233-->
END%%
%%ANKI
Basic
Given `int32_t x = 0x89ABCDEF`, what is the value of `x & 0xFF`?
Back: `0x000000EF`
Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
<!--ID: 1707774068237-->
END%%
## References
* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.

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notes/logic/equiv-trans.md
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@ -122,7 +122,7 @@ END%%
%%ANKI
Basic
What C operator corresponds to $\neg$?
What C logical operator corresponds to $\neg$?
Back: `!`
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
@ -131,7 +131,7 @@ END%%
%%ANKI
Basic
What C operator corresponds to $\land$?
What C logical operator corresponds to $\land$?
Back: There isn't one.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
@ -140,7 +140,7 @@ END%%
%%ANKI
Basic
What C operator corresponds to $\lor$?
What C logical operator corresponds to $\lor$?
Back: There isn't one.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
@ -149,7 +149,7 @@ END%%
%%ANKI
Basic
What C operator corresponds to $\Rightarrow$?
What C logical operator corresponds to $\Rightarrow$?
Back: There isn't one.
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c
@ -158,7 +158,7 @@ END%%
%%ANKI
Basic
What C operator corresponds to $\Leftrightarrow$?
What C logical operator corresponds to $\Leftrightarrow$?
Back: `==`
Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
Tags: c