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Topics referred to by the same term
Binary logic may refer to: Boolean logic, a two-valued formal logic Logic gates implementing Boolean logic in digital electronics Bivalent logic or two-valued
Binary_logic
Device performing a Boolean function
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output
Logic_gate
Computer programming language
Binary combinatory logic (BCL) is a computer programming language that uses binary terms 0 and 1 to create a complete formulation of combinatory logic
Binary_combinatory_logic
Finite states of a digital signal
depends on the logic family being used. A logic-level shifter can be used to allow compatibility between different circuits. In binary logic the two levels
Logic_level
Digital circuit that produces sums from inputs
more logic around the basic adder. George Stibitz invented the 2-bit binary adder (the Model K) in 1937. The half adder adds two single binary digits
Adder_(electronics)
Electronic circuit used to multiply binary numbers
A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic
Binary_multiplier
Signal used to represent data as a sequence of discrete values
the signal can have two possible valid values; this is called a binary signal or logic signal. They are represented by two voltage bands: one near a reference
Digital_signal
Number expressed in the base-2 numeral system
as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used
Binary_number
Symbols representing logical operations
sixteen possible binary truth functions of logic. The logic alphabet was developed by Shea Zellweger. The major emphasis of his iconic "logic alphabet" is
Logic_alphabet
Data whose unit can take on only two possible states
digit) in computer science, truth value in mathematical logic and related domains and binary variable in statistics. A discrete variable that can take
Binary_data
Type of probabilistic logic
Subjective logic is a type of probabilistic logic that explicitly takes epistemic uncertainty and source trust into account. In general, subjective logic is suitable
Subjective_logic
System including an indeterminate value
) Similarly, where Boolean logic has 22×2 = 16 distinct binary operators (operators with 2 inputs) possible, ternary logic has 33×3 = 19,683 such operators
Three-valued_logic
Soviet ternary computer
balanced ternary numeral system and three-valued ternary logic instead of the two-valued binary logic prevalent in other computers. The computer was built
Setun
Encoded data represented in binary notation
Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Boole's system was based on binary, a yes-no, on-off
Binary_code
Computer that uses ternary logic
ternary logic (i.e., base 3) instead of the more common binary system (i.e., base 2) in its calculations. Ternary computers use trits, instead of binary bits
Ternary_computer
Leibniz developed logic in a formal, mathematical sense with his writings on the binary numeral system. Leibniz simplified the binary system and articulated
History_of_computer_science
English mathematician and philosopher (1815–1864)
revolutionizing logic by transforming it from a philosophical study of language into a mathematical system of algebraic equations using binary values and logical
George_Boole
Combinational digital circuit
an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is
Arithmetic_logic_unit
Base-3 numeral system
to how octal and hexadecimal systems are used in place of binary. In certain analog logic, the state of the circuit is often expressed ternary. This
Ternary_numeral_system
Reconfigurable digital circuit element
"fixed-OR, programmable-AND" plane used to implement "sum-of-products" binary logic equations for each of the outputs in terms of the inputs and either synchronous
Programmable_logic_device
Programming language for industrial controllers
Ladder logic was originally a written method to document the design and construction of relay racks as used in manufacturing and process control. Each
Ladder_logic
Ordering of binary values, used for positioning and error correction
simplify logic operations and reduce errors in practice. Many devices indicate position by closing and opening switches. If that device uses natural binary codes
Gray_code
Type of logical system
first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified
First-order_logic
Logic gate
EXOR and pronounced as exclusive OR, ksor or sometimes EX-OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs
XOR_gate
Field-programmable semiconductor devices
"fixed-OR, programmable-AND" plane used to implement "sum-of-products" binary logic equations for each of the outputs in terms of the inputs and either synchronous
Programmable_Array_Logic
Limited form of tree data structure
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child
Binary_tree
System of digitally encoding numbers
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a
Binary-coded_decimal
Logic with discrete truth values
values are discrete. Traditionally, in Aristotle's logic, the bivalent logic, also known as binary logic was the norm, as the law of the excluded middle
Finite-valued_logic
Algebraic manipulation of "true" and "false"
functions known as (reduced ordered) binary decision diagrams (BDD) for logic synthesis and formal verification. Logic sentences that can be expressed in
Boolean_algebra
Type of formal logic
future. Additional binary operators are also relevant to temporal logics (see Linear temporal logic). Versions of temporal logic can be used in computer
Modal_logic
Symbol connecting formulas in logic
arithmetic expressions. For instance, in the syntax of propositional logic, the binary connective ∨ {\displaystyle \lor } (meaning "or") can be used to join
Logical_connective
Basic circuit in quantum computing
computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic gates are the building
Quantum_logic_gate
Types of approximate algorithm
Fuzzy logic is a computational paradigm that entertains the uncertainties in data by using levels of truth rather than rigid 0s and 1s in binary. Next
Soft_computing
Reasoning about equations with free variables
Johns Hopkins University, published "On the Algebra of Logic". Logic turned more algebraic when binary relations were combined with composition of relations
Algebraic_logic
Topics referred to by the same term
middle ground Gender binary, the classification of gender into two distinct and disconnected forms of masculine and feminine Binary logic (disambiguation)
Binary
Logical connective AND
logic gate type And-inverter graph – Graph representing an implementation of the logical functionality of a network Bitwise AND – Bit-by-bit binary operation
Logical_conjunction
Concept in mathematical logic
logic gates can be assembled from either only binary NAND gates, or only binary NOR gates. Modern texts on logic typically take as primitive some subset of
Functional_completeness
Combinational logic circuit
In digital electronics, a binary decoder is a combinational logic circuit that converts binary information from the n coded inputs to a maximum of 2n unique
Binary_decoder
Mathematical table used in logic
gives definitions of each of the 7 basic logic gate functions of two Boolean variables P and Q: For binary operators, a condensed form of truth table
Truth_table
IEEE standard that defines logic values used in electronic design
be. HDL synthesis tools usually produce circuits that operate only on binary logic. When designing a digital circuit, some conditions may be outside the
IEEE_1164
Topics referred to by the same term
(disambiguation), in mathematics Propositional logic, a system of evaluating truth-based propositions in terms of binary logic PL (complexity), in complexity theory
PL
True when either but not both inputs are true
introduced a system of Polish notation that names all 16 binary connectives of classical logic which is a compatible extension of the notation of Łukasiewicz
Exclusive_or
Device storing number of times an event or process occurred
In digital electronics, a counter is a sequential logic circuit that counts and stores the number of positive or negative transitions of a clock signal
Counter_(digital)
AND and OR logic with diodes and resistors
logic can only implement OR and AND, because inverters (NOT gates) require an active device. Main article: Logic level § 2-level logic Binary logic uses
Diode_logic
Arithmetic logic circuit
propagate bits are used by the carry-lookahead logic, it doesn't matter which definition is used. In the case of binary addition, this definition is expressed
Carry-lookahead_adder
System for reasoning about vagueness
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept
Fuzzy_logic
Prefix indicating a power of two
A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes
Binary_prefix
Assignment of meaning to the symbols of a formal language
order logic and other predicate logics. There are two general approaches. The first approach is to treat equality as no different than any other binary relation
Interpretation_(logic)
Process in digital electronics and integrated circuit design
form etc. Logic optimization algorithms generally work either on the structural (SOPs, factored form) or functional representation (binary decision diagrams
Logic_optimization
Logical operation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition
Negation
T-norm fuzzy logics are a family of non-classical logics, informally delimited by having a semantics that takes the real unit interval [0, 1] for the
T-norm_fuzzy_logics
Approach to logic
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to
Term_logic
Relationship between elements of two sets
In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set (possibly the same) called the
Binary_relation
Any logic with four truth values
calculus, theorems and so on) with communication protocols built using binary logic and displaying responses with four possible states implemented with Boolean-like
Four-valued_logic
In logic, a statement which is always true
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms
Tautology_(logic)
Propositional calculus in which there are more than two truth values
Many-valued logic (also multi- or multiple-valued logic) is a propositional or predicate calculus in which there are more than two truth values. Traditionally
Many-valued_logic
Logic gate implementing negation
it produces the ones' complement of a binary number, swapping 0s and 1s. The NOT gate is one of three basic logic gates from which any Boolean circuit
Inverter_(logic_gate)
Digital logic circuit
flip-flop, coincident flip-flop, or two-hand safety circuit) is a small binary logic circuit widely used in design of asynchronous circuits and systems. It
C-element
Digital audio workstation
Notator Logic, or Logic, by German software developer C-Lab which later went by Emagic. Apple acquired Emagic in 2002 and rebranded Logic to Logic Pro, adding
Logic_Pro
Variation to BCD-code where three (11) is added to a binary representation
Excess-3, 3-excess or 10-excess-3 binary code (often abbreviated as XS-3, 3XS or X3), shifted binary or Stibitz code (after George Stibitz, who built a
Excess-3
Category of modern incarnations of Orientalist thinking
Orientalism, criticised as being "monolithic, totalizing, reliant on a binary logic, and based on an assumption of moral and cultural superiority over the
Neo-orientalism
The following is a list of CMOS 4000-series digital logic integrated circuits. In 1968, the original 4000-series was introduced by RCA. Although more
List of 4000-series integrated circuits
List_of_4000-series_integrated_circuits
Property that assigns truth values to k-tuples of individuals
by Rx1⋯xn and using postfix notation by x1⋯xnR. In the case where R is a binary relation, those statements are also denoted using infix notation by x1Rx2
Finitary_relation
Mathematical operation with two operands
In mathematics, a binary operation or dyadic operation is a kind of binary function, i.e. given a pair of input values (called operands), it produces an
Binary_operation
Programmable machine that processes data
service life. Transistorized computers could contain tens of thousands of binary logic circuits in a relatively compact space. However, early junction transistors
Computer
Form of logic that allows quantification over predicates
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic
Second-order_logic
Argument whose conclusion must be true if its premises are
framework of classical logic. However, within that system 'true' and 'false' essentially function more like mathematical states such as binary 1s and 0s than
Validity_(logic)
Mapping of mathematical formulas to a particular meaning
structures are the objects used to define the semantics of first-order logic, cf. also Tarski's theory of truth or Tarskian semantics. For a given theory
Structure (mathematical logic)
Structure_(mathematical_logic)
Type of category in mathematics
initial object, binary coproducts and binary coequalizers. E {\displaystyle {\mathcal {E}}} has exponential objects (in addition to binary products, which
Elementary_topos
Function in logic
referred to as an operator. In two-valued logic there are 2 nullary operators (constants), 4 unary operators, 16 binary operators, 256 ternary operators, and
Truth_function
Form of second-order logic
second-order logic is undecidable in general because this logic subsumes first-order logic. The monadic second-order theory of the infinite complete binary tree
Monadic_second-order_logic
Mechanical computer
Boolean logic operations. With a three binary digit (3-bit) readout of the state of the flip-flops, it could be programmed to demonstrate binary logic, to
Digi-Comp_I
Symbol representing a property or relation in logic
In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all.
Predicate_(logic)
Fragment of first-order logic
nonempty domains). Adding a single binary relation symbol to monadic logic, however, results in an undecidable logic. The formal system described above
Monadic_predicate_calculus
Number of arguments required by a function
Mathematics portal Philosophy portal Logic of relatives Binary relation Ternary relation Theory of relations Signature (logic) Parameter p-adic number Cardinality
Arity
Model of quantum computation
could function in a similar fashion to traditional digital computing binary logic gates. Iriyama, Ohya, and Volovich have developed a model of a linear
Quantum_Turing_machine
Framework of distances and directions
even though both terms offer a way to think outside the terms of a binary logic. Bhabha's Third Space is the space in which hybrid cultural forms and
Space
Intellectual current and methodological approach in the social science
general—cannot be reduced to logical organizations on the basis of the binary logic of oppositions. Critical theorist Jürgen Habermas (1985) accused structuralists
Structuralism
System for representing and reasoning about time
In logic, a temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example
Temporal_logic
substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also
BL_(logic)
Political ideology emphasising the "common people"
discursive strategies often play into the hands of populists, reinforcing the binary logic—"the pure people" versus "the corrupt elite"—on which they believe populism
Populism
Subfield of mathematics
Mathematical logic is the study of logic within mathematics. This is commonly done by means of formal systems called formal logics that define rules of
Mathematical_logic
Function that preserves distinctness
v t e Mathematical logic General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma
Injective_function
American artist (1934–2024)
together. "The binary logic of the west takes on an added dimension when confronted with the presence of a black woman." Behind the binary logic of science
Lorraine_O'Grady
Logical formulation of recursion
In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development
Fixed-point_logic
first binary adder. Typically signals have two states – low (usually representing 0) and high (usually representing 1), but sometimes three-valued logic is
History_of_computing_hardware
Electronic circuits that utilize digital signals
also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it was the invention of
Digital_electronics
Model of logic based on matrix algebra
Classic binary logic is represented by a small set of mathematical functions depending on one (monadic) or two (dyadic) variables. In the binary set, the
Vector_logic
Pair of related terms or concepts that are opposite in meaning
A binary opposition (also binary system) is a pair of related terms or concepts that are opposite in meaning. Binary opposition is the system of language
Binary_opposition
Computer data variable
programming, a flag can refer to one or more bits that are used to store a binary value or a Boolean variable for signaling special code conditions, such
Flag_(programming)
Varying application boundaries
regard fuzzy logic merely as an extension of Boolean logic (a two-valued logic or binary logic is simply replaced with a many-valued logic). However, Boolean
Fuzzy_concept
Multidrop serial communication standard
defines the logic states 1 (off) and 0 (on), by the polarity between A and B terminals. If A is negative with respect to B, the state is binary 1. The reversed
RS-485
Computing circuit
circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that adds or subtracts depending on a control signal
Adder–subtractor
Instrument for measuring, keeping or indicating time
integrated circuit counters or dividers add the pulses up digitally, using binary logic. Often pushbuttons on the case allow the hour and minute counters to
Clock
Overview of and topical guide to logic
Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal
Outline_of_logic
Class of formal logics
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had
Classical_logic
1982 educational video game
open-ended area to design one's own logic circuits and "games". The colors of orange and white are used to show the binary logic states of 1 and 0. As the circuits
Rocky's_Boots
Classic NP-complete problem in computer science
certain problems, and provides us with an alternative to dual-rail and binary logic reductions. The gadgets that such a reduction needs to construct are:
Circuit satisfiability problem
Circuit_satisfiability_problem
Unit of information
information in computing and digital communication. The name is a portmanteau of binary digit. Its symbol is either "bit" (IEC standard) or lowercase "b" (IEEE
Bit
Clock designed to keep time for 10,000 years
of friction. Instead, the clock uses binary digital logic, implemented mechanically in a sequence of stacked binary adders (or as their inventor, Hillis
Clock_of_the_Long_Now
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