- "First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers."
A mathematical system used to express logic functions, based on the binary values of 0 and 1.
Binary Number System: This is the foundation of Boolean algebra that deals with representing numbers and data in binary form.
Logical Operators: These are operators such as AND, OR and NOT that are used to define Boolean expressions.
Boolean Expressions: These are expressions that use Boolean operators to describe logical operations.
Truth Tables: These are tables that define the results of logical operations in terms of all possible inputs.
Laws of Boolean Algebra: These are a set of laws that govern the manipulation of Boolean expressions.
Simplification of Boolean Expressions: This involves using the laws of Boolean algebra to simplify expressions and reduce the number of terms.
Combinational Logic: This is logic that involves only the current input values and not the past input values.
Sequential Logic: This logic involves the past and current input values and can be used to create memory elements.
Logic Gates: These are basic components of digital circuits that perform logical operations.
De Morgan's Theorems: These are two theorems that relate the negation of a conjunction (AND) or disjunction (OR) to the conjunction or disjunction of the negations.
Karnaugh Maps: This is a graphical method used for simplifying Boolean expressions.
Boolean Functions: These are functions that take Boolean inputs and return Boolean outputs.
MinTerms, MaxTerms and Canonical Forms: These are three different ways to represent Boolean functions.
Boolean Algebra in Computers: This involves the application of Boolean algebra in computer architecture and digital circuits.
- "Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬."
- "Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division."
- "Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854)."
- "According to Huntington, the term 'Boolean algebra' was first suggested by Henry M. Sheffer in 1913..."
- "Charles Sanders Peirce gave the title 'A Boolian [sic] Algebra with One Constant' to the first chapter of his 'The Simplest Mathematics' in 1880."
- "Boolean algebra has been fundamental in the development of digital electronics..."
- "It is also used in set theory and statistics."
- "The values of the variables are the truth values true and false, usually denoted 1 and 0..."
- "Boolean algebra is therefore a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations."
- "...and set forth more fully in his An Investigation of the Laws of Thought (1854)."
- "According to Huntington, the term 'Boolean algebra' was first suggested by Henry M. Sheffer in 1913..."
- "Boolean algebra...is provided for in all modern programming languages."
- "George Boole...introduced Boolean algebra in his first book The Mathematical Analysis of Logic (1847)..."
- "Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. It is also used in set theory and statistics."
- "Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division."
- "Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847)..."
- "Charles Sanders Peirce gave the title 'A Boolian [sic] Algebra with One Constant' to the first chapter of his 'The Simplest Mathematics' in 1880."
- "Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬."
- "The values of the variables are the truth values true and false, usually denoted 1 and 0..."