274 lines
8.5 KiB
Markdown
274 lines
8.5 KiB
Markdown
---
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title: Boolean Algebra
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TARGET DECK: Obsidian::STEM
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FILE TAGS: logic::boolean
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tags:
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- logic
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- boolean
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---
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## Overview
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**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 ($\lor$).
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%%ANKI
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Basic
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What name is given to $\land$ operands?
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Back: Conjuncts.
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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<!--ID: 1706994861304-->
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END%%
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%%ANKI
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Basic
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What set operation parallels conjunction?
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Back: $\cap$
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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<!--ID: 1708221293474-->
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END%%
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%%ANKI
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Basic
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What name is given to $\lor$ operands?
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Back: Disjuncts.
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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<!--ID: 1706994861306-->
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END%%
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%%ANKI
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Basic
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What set operation parallels disjunction?
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Back: $\cup$
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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<!--ID: 1708221293479-->
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END%%
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%%ANKI
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Basic
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What C logical operator corresponds to $\neg$?
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Back: `!`
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Tags: c17
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<!--ID: 1706994861325-->
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END%%
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%%ANKI
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Basic
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What C logical operator corresponds to $\land$?
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Back: N/A
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Tags: c17
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<!--ID: 1706994861327-->
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END%%
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%%ANKI
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Basic
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What C logical operator corresponds to $\lor$?
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Back: N/A
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Tags: c17
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<!--ID: 1706994861329-->
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END%%
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%%ANKI
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Basic
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What C logical operator corresponds to $\Rightarrow$?
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Back: N/A
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Tags: c17
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<!--ID: 1706994861331-->
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END%%
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%%ANKI
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Basic
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What C logical operator corresponds to $\Leftrightarrow$?
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Back: `==`
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Tags: c17
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<!--ID: 1706994861333-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to $\neg$?
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Back: `~`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068116-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to $\land$?
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Back: `&`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068124-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to $\lor$?
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Back: `|`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068132-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to $\oplus$?
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Back: `^`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068137-->
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END%%
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%%ANKI
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Basic
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What is the value of `~0b00001111`?
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Back: `0b11110000`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068142-->
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END%%
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%%ANKI
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Basic
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What is the value of `0b00001111 & 0b11111111`?
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Back: `0b00001111`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068151-->
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END%%
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%%ANKI
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Basic
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What is the value of `0b00001111 | 0b11111111?
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Back: `0b11111111`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068161-->
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END%%
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%%ANKI
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Basic
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What is the value of `0b00001111 ^ 0b11111111`?
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Back: `0b11110000`
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Reference: 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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Tags: binary c17
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<!--ID: 1707774068167-->
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END%%
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%%ANKI
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Basic
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How do bit vectors represent finite sets?
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Back: A `1` bit-value indicates membership at the given index.
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Reference: 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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Tags: binary
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<!--ID: 1707774068173-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to set complement?
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Back: `~`
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Reference: 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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Tags: binary c17 set
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<!--ID: 1707774068179-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to set notation $\cup$?
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Back: `|`
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Reference: 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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Tags: binary c17 set
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<!--ID: 1707774068186-->
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END%%
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%%ANKI
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Cloze
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{$\cup$} is to the algebra of sets whereas {$\lor$} is to boolean algebra.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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Tags: set
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<!--ID: 1717554445676-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to set notation $\cap$?
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Back: `&`
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Reference: 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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Tags: binary c17 set
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<!--ID: 1707774068192-->
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END%%
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%%ANKI
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Cloze
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{$\cap$} is to the algebra of sets whereas {$\land$} is to boolean algebra.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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Tags: set
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<!--ID: 1717554445682-->
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END%%
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%%ANKI
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Basic
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What C bit-level operator corresponds to set notation $\triangle$?
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Back: `^`
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Reference: 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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Tags: binary c17 set
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<!--ID: 1717554445689-->
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END%%
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%%ANKI
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Cloze
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{$\triangle$} is to the algebra of sets whereas {$\oplus$} is to boolean algebra.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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Tags: set
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<!--ID: 1717554445695-->
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END%%
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%%ANKI
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Basic
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What is a bit mask?
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Back: A bit pattern that selects certain bits of a data type.
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Reference: 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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<!--ID: 1707774068217-->
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END%%
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%%ANKI
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Basic
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What hexadecimal bit mask returns the least significant byte of a word?
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Back: `0xFF`
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Reference: 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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<!--ID: 1707774068225-->
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END%%
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%%ANKI
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Basic
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What portable expression yields a mask of all ones, regardless of data type?
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Back: `~0`
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Reference: 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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<!--ID: 1707774068229-->
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END%%
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%%ANKI
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Basic
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Why might you prefer `~0` over e.g. `0xFFFFFFFF`?
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Back: The former is independent of data type.
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Reference: 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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<!--ID: 1707774068233-->
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END%%
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%%ANKI
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Basic
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Given `int32_t x = 0x89ABCDEF`, what is the value of `x & 0xFF`?
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Back: `0x000000EF`
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Reference: 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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<!--ID: 1707774068237-->
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END%%
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## Bibliography
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* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. |