Boolean logic


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Boolean logic

(mathematics)

Boolean logic

The "mathematics of logic," developed by English mathematician George Boole in the mid-19th century. Just as add, subtract, multiply and divide are the primary operations of arithmetic, AND, OR and NOT are the primary operations of Boolean logic and building blocks of every digital circuit. Other common variations are derived from these three logical operators (see NAND, NOR and XOR). See Boolean search, binary, logic gate and Bebop to the Boolean Boogie.


Decimal Vs. Binary
Decimal arithmetic holds 10 values (0 to 9) in each digit position. In binary, there are only two (0 and 1). Note below the four possible result and carry bits when adding two binary digits (bits) together.


AND, OR and NOT Gates
Transistors wired in series and parallel patterns make up these "gates," which accept inputs of 0 (no pulse) or 1 (a pulse) and generate outputs of 0 or 1. While AND requires that both inputs are 1 to generate an output of 1, OR only needs one input to be 1. NOT reverses the input. For a conceptual diagram of these actions, see Boolean gates.



Decimal Vs. Binary
Decimal arithmetic holds 10 values (0 to 9) in each digit position. In binary, there are only two (0 and 1). Note below the four possible result and carry bits when adding two binary digits (bits) together.







Add a One and Zero
Trace the red 1 (pulse, current) and white 0 (no pulse, no current) through the gates and notice their outputs. This half-adder circuit is in every CPU.


Add a One and Zero
Trace the red 1 (pulse, current) and white 0 (no pulse, no current) through the gates and notice their outputs. This half-adder circuit is in every CPU.







Trace the Flow Yourself
Choose any two binary digits as input and trace them through this half-adder circuit (0 is no current; 1 is current). Watch how the output is generated.


Trace the Flow Yourself
Choose any two binary digits as input and trace them through this half-adder circuit (0 is no current; 1 is current). Watch how the output is generated.







Patterns of Boolean Logic
Transistors, which are depicted here as mechanical switches, make up gates. Gates make up circuits, and circuits make up every digital device. There are billions of transistors in modern chips, and they fit in an area the size of a postage stamp. For more details on this mechanical conceptualization, see Boolean gates. See transistor and chip.
References in periodicals archive ?
The Option nodes basically represent the OR boolean logic operations.
i) Human judgments, such as attitude judgments, are often not simply read out from memory, but rather, they are constructed from the cognitive state for the question at hand; and (ii) drawing a conclusion from one question changes the context and disturbs the cognitive system, which then (iii) affects the answer to the next question, producing order effects, so that (iv) human judgments do not always obey the commutative rule of Boolean logic.
Simply put, Boolean logic is the algebraic interpretation of truth tables.
We also developed fixed QCA circuit which can be used to get all Boolean logic functions and also to build combinational circuits such as comparators, parity generators and checkers.
Erosion and dilation are defined in agreement with the truth value of these propositions (0 or 1); therefore, Boolean logic is present in these definitions.
Black-and-white diagrams and boolean logic symbols help drive the precepts home, though Artificial Intelligence For Computer Games does not contain any computer code per se--this is a manual of basic techniques that can generalize to any programming system.
Capable of many sophisticated sequences of operations, the system's field configuration program is based on Boolean logic statements.
One of the most commonly used search principles is Boolean logic, which refers to the logical relationship among search terms.
Mechanics of searching, including Boolean logic and truncation.
Even in doctoral seminars that I teach, I find the need to explain Boolean logic and patiently teach students how to develop search strategies, formulate queries, and even how to compute the precision of searches.
Without having to learn Boolean logic or wrestle with if-then-else logic, Dewqs' NMS makes it easy to rid your inbox of unwanted emails.
Boolean logic can be used to search by keyword, date, format, language, title, author, subject, or any combination of these.