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Adder (electronics)
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of microprocessor, processors, adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate address space, addresses, database index, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. History George Stibitz invented the 2-bit binary adder (the Model K (calculator), Model K) in 1937. Binary adders Half adder The half adder adds two single binary digits A and B. It has two outputs, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Circuit
In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain and the values the gates can produce. For example, the values in a Boolean circuit are Boolean values, and the circuit includes conjunction, disjunction, and negation gates. The values in an integer circuit are sets of integers and the gates compute set union, set intersection, and set complement, as well as the arithmetic operations addition and multiplication. Formal definition A circuit is a triplet (M, L, G), where * M is a set of values, * L is a set of gate labels, each of which is a function from M^ to M for some non-negative integer i (where i represents the number of inputs to the gate), and * G is a labelled graph, labelled directed acyclic gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Stibitz
George Robert Stibitz (April 30, 1904 – January 31, 1995) was an American researcher at Bell Labs who is internationally recognized as one of the fathers of the modern digital computer. He was known for his work in the 1930s and 1940s on the realization of Boolean logic digital circuits using electromechanical relays as the switching element. Early life and education Stibitz was born in York, Pennsylvania, the son of Mildred Murphy, a math teacher, and George Stibitz, a Reformed Church in the United States, German Reformed minister and theology professor. Throughout his childhood, Stibitz enjoyed assembling devices and systems, working with material as diverse as a toy Meccano set or the electrical wiring of the family home. He received a bachelor's degree in mathematics from Denison University in Granville, Ohio, a master's degree in physics from Union College in 1927, and a Ph.D. in mathematical physics from Cornell University in 1930 with a thesis entitled "Vibrations of a N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAND Gates
In digital electronics, a NAND (NOT AND) gate is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan's laws, a two-input NAND gate's logic may be expressed as \overline \lor \overline = \overline, making a NAND gate equivalent to inverters followed by an OR gate. The NAND gate is significant because any Boolean function can be implemented by using a combination of NAND gates. This property is called "functional completeness". It shares this property with the NOR gate. Digital systems employing certain logic circuits take advantage of NAND's functional completeness. NAND gates with two or more inputs are available as integrated circuits in transistor–transistor logic, CMOS, and other logic fami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Completeness
In Mathematical logic, logic, a functionally complete set of logical connectives or Boolean function, Boolean operators is one that can be used to express all possible truth tables by combining members of the Set (mathematics), set into a Boolean expression.. ("Complete set of logical connectives").. ("[F]unctional completeness of [a] set of logical operators"). A well-known complete set of connectives is . Each of the singleton (mathematics), singleton sets and is functionally complete. However, the set is incomplete, due to its inability to express NOT. A gate (or set of gates) that is functionally complete can also be called a universal gate (or a universal set of gates). In a context of propositional logic, functionally complete sets of connectives are also called (''expressively'') ''adequate''.. (Defines "expressively adequate", shortened to "adequate set of connectives" in a section heading.) From the point of view of digital electronics, functional completeness means t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karnaugh Map
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which itself was a rediscovery of Allan Marquand's 1881 ''logical diagram'' or Marquand diagram. They are also known as Marquand–Veitch diagrams, Karnaugh–Veitch (KV) maps, and (rarely) Svoboda charts. An early advance in the history of formal logic methodology, Karnaugh maps remain relevant in the digital age, especially in the fields of logical circuit design and digital engineering. Definition A Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions. The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transistor
A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semiconductor material, usually with at least three terminal (electronics), terminals for connection to an electronic circuit. A voltage or Electric current, current applied to one pair of the transistor's terminals controls the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Some transistors are packaged individually, but many more in miniature form are found embedded in integrated circuits. Because transistors are the key active components in practically all modern electronics, many people consider them one of the 20th century's greatest inventions. Physicist Julius Edgar Lilienfeld proposed the concept of a field-effect transisto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Symbol
An electronic symbol is a pictogram used to represent various electrical and electronic devices or functions, such as wires, batteries, resistors, and transistors, in a schematic diagram of an electrical or electronic circuit. These symbols are largely standardized internationally today, but may vary from country to country, or engineering discipline, based on traditional conventions. Standards for symbols The graphic symbols used for electrical components in circuit diagrams are covered by national and international standards, in particular: * IEC 60617 (also known as BS 3939). * There is also IEC 61131-3 – for ladder-logic symbols. * JIC JIC (Joint Industrial Council) symbols as approved and adopted by the NMTBA (National Machine Tool Builders Association). They have been extracted from the Appendix of the NMTBA Specification EGPl-1967. * ANSI Y32.2-1975 (also known aIEEE Std 315-1975or CSA Z99-1975). * IEEE Std 91/91a: graphic symbols for logic functions (used in digital ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAND Gate
In digital electronics, a NAND (NOT AND) gate is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan's laws, a two-input NAND gate's logic may be expressed as \overline \lor \overline = \overline, making a NAND gate equivalent to inverters followed by an OR gate. The NAND gate is significant because any Boolean function can be implemented by using a combination of NAND gates. This property is called "functional completeness". It shares this property with the NOR gate. Digital systems employing certain logic circuits take advantage of NAND's functional completeness. NAND gates with two or more inputs are available as integrated circuits in transistor–transistor logic, CMOS, and other logi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schematic
A schematic, or schematic diagram, is a designed representation of the elements of a system using abstract, graphic symbols rather than realistic pictures. A schematic usually omits all details that are not relevant to the key information the schematic is intended to convey, and may include oversimplified elements in order to make this essential meaning easier to grasp, as well as additional organization of the information. For example, a subway map intended for passengers may represent a subway station with a dot. The dot is not intended to resemble the actual station at all but aims to give the viewer information without unnecessary visual clutter. A schematic diagram of a chemical process uses symbols in place of detailed representations of the vessels, piping, valves, pumps, and other equipment that compose the system, thus emphasizing the functions of the individual elements and the interconnections among them and suppresses their physical details. In an electronic circuit d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of the operation for those values. A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful for mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OR Gate
The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by different voltage levels. Description Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of these inputs are 1, or outputs a 0 only if all inputs are 0. The inputs and outputs are binary digits ("bits") which have two possible truth value, logical states. In addition to 1 and 0, these states may be called true and false, high and low, active and inactive, or other such pairs of symbols. Thus it performs a logical disjunction (∨) from mathematical logic. The gate can be represented with the plus sign (+) because it can be used for Disjunction introduction, logical addition. Equivalently, an OR gate finds the ''maximum'' between two binary digits, just as the AND gate finds the ''minimum''. Together with the AND gate and the NOT gate, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AND Gate
The AND gate is a basic digital logic gate that implements the logical conjunction (∧) from mathematical logic AND gates behave according to their truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If any of the inputs to the AND gate are not HIGH, a LOW (0) is outputted. The function can be extended to any number of inputs by multiple gates up in a chain. Symbols There are three symbols for AND gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN symbol. Additional inputs can be added as needed. For more information see the Logic gate symbols article. It can also be denoted as symbol "^" or "&". The AND gate with inputs ''A'' and ''B'' and output ''C'' implements the logical expression C = A \cdot B. This expression also may be denoted as C=A \wedge B or C=A \And B. As of Unicode 16.0.0, the AND gate is also encoded in the Symbols for Legacy Computing Su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
