notebook/notes/algebra/boolean.md

title	TARGET DECK	FILE TAGS	tags
Boolean Algebra	Obsidian::STEM	logic::boolean	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 name is given to \land operands? Back: Conjuncts. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

END%%

%%ANKI Basic What set operation parallels conjunction? Back: \cap Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

END%%

%%ANKI Basic What name is given to \lor operands? Back: Disjuncts. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

END%%

%%ANKI Basic What set operation parallels disjunction? Back: \cup Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.

END%%

%%ANKI Basic 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: c17

END%%

%%ANKI Basic What C logical operator corresponds to \land? Back: N/A. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981. Tags: c17

END%%

%%ANKI Basic What C logical operator corresponds to \lor? Back: N/A. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981. Tags: c17

END%%

%%ANKI Basic What C logical operator corresponds to \Rightarrow? Back: N/A. Reference: Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981. Tags: c17

END%%

%%ANKI Basic 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: c17

END%%

%%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 c17

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 c17

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 c17

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 c17

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 c17

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 c17

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 c17

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 c17

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

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 c17 set

END%%

%%ANKI Basic What C bit-level operator corresponds to set notation \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 c17 set

END%%

%%ANKI Cloze {\cup} is to the algebra of sets whereas {\lor} is to boolean algebra. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977). Tags: set

END%%

%%ANKI Basic What C bit-level operator corresponds to set notation \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 c17 set

END%%

%%ANKI Cloze {\cap} is to the algebra of sets whereas {\land} is to boolean algebra. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977). Tags: set

END%%

%%ANKI Basic What C bit-level operator corresponds to set notation \triangle? 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 c17 set

END%%

%%ANKI Cloze {\triangle} is to the algebra of sets whereas {\oplus} is to boolean algebra. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977). Tags: set

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.

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.

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.

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.

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.

END%%

Bibliography

• Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.