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OR-AND-invert
OR-AND-invert gates, or OAI-gates, are logic gates comprising OR gates followed by a NAND gate. They can be efficiently implemented in logic families like CMOS and Transistor–transistor logic, TTL. They are Duality_(mathematics)#Duality_in_logic_and_set_theory, dual to AND-OR-invert gates. Overview OR-AND-invert gates implement the inverted product of sums. n groups of m_i, m_i \ge 1, i=1\ldots n input signals combined with OR gate, OR, and the results then combined with NAND gate, NAND. Examples 2-1 OAI-gate A 2-1-OAI gate realizes the following function: : Y = \overline 2-2 OAI gate A 2-2-OAI gate realizes the following function: : Y = \overline Realization OAI-gates can efficiently be implemented as complex gates. An example of a 3-1 OAI-gate is shown in the figure below. Examples of use One possibility of implementing an XOR gate is by using a 2-2-OAI-gate with non-inverted and inverted inputs. References [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XOR Gate
XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive disjunction, exclusive or (\nleftrightarrow) from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both". An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as a Inverter (logic gate), inverter (a NOT gate) which may be activated or deactivated by a switch. XOR can also be viewed as addition Modular arithmetic, modulo 2. As a result, XOR gates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AND-OR-invert
AND-OR-invert (AOI) logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more AND gates followed by a NOR gate (equivalent to an OR gate through an Inverter gate, which is the "OI" part of "AOI"). Construction of AOI cells is particularly efficient using CMOS technology, where the total number of transistor gates can be compared to the same construction using NAND logic or NOR logic. The complement of AOI logic is OR-AND-invert (OAI) logic, where the OR gates precede a NAND gate. Overview Most logic optimization result in a Canonical normal form, sum-of-products or product-of-sums logic expression. AOI is used for sum-of-products, the variables are ANDed to form minterms which are ORed together then inverted: * is known as a AOI 2-1 gate. * is known as a AOI 2-2 gate. * is known as a AOI 3-3 gate. * is known as a AOI 4-4 gate. * is known as a AOI 4-3-2 gate. * and other variations. Examples AOI gates perform one or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Gates
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more Binary number, binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see ideal and real op-amps for comparison). The primary way of building logic gates uses diodes or transistors acting as electronic switches. Today, most logic gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). ''From Integrated circuit'' They can also be constructed using vacuum tubes, electromagnetic relays with relay logic, fluidic logic, pneumatics#Pneumatic logic, pneumatic logic, optics, molecular logic gate, molecules, acoustics, or even Analytical Engine, mechanical or thermal elements. Logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the constr ... [...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] |
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] |
CMOS
Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss ", , ) is a type of MOSFET, metal–oxide–semiconductor field-effect transistor (MOSFET) semiconductor device fabrication, fabrication process that uses complementary and symmetrical pairs of p-type semiconductor, p-type and n-type semiconductor, n-type MOSFETs for logic functions. CMOS technology is used for constructing integrated circuit (IC) chips, including microprocessors, microcontrollers, memory chips (including Nonvolatile BIOS memory, CMOS BIOS), and other digital logic circuits. CMOS technology is also used for analog circuits such as image sensors (CMOS sensors), data conversion, data converters, RF circuits (RF CMOS), and highly integrated transceivers for many types of communication. In 1948, Bardeen and Brattain patented an insulated-gate transistor (IGFET) with an inversion layer. Bardeen's concept forms the basis of CMOS technology today. The CMOS process was presented by Fairchild Semico ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transistor–transistor Logic
Transistor–transistor logic (TTL) is a logic family built from bipolar junction transistors (BJTs). Its name signifies that transistors perform both the logic function (the first "transistor") and the amplifying function (the second "transistor"), as opposed to earlier resistor–transistor logic (RTL) and diode–transistor logic (DTL). TTL integrated circuits (ICs) were widely used in applications such as computers, industrial controls, test equipment and instrumentation, consumer electronics, and synthesizers. After their introduction in integrated circuit form in 1963 by Sylvania Electric Products, TTL integrated circuits were manufactured by several semiconductor companies. The 7400 series by Texas Instruments became particularly popular. TTL manufacturers offered a wide range of logic gates, flip-flops, counters, and other circuits. Variations of the original TTL circuit design offered higher speed or lower power dissipation to allow design optimization. TTL devices w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Duality (mathematics)
In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is , then the dual of is . In other cases the dual of the dual – the double dual or bidual – is not necessarily identical to the original (also called ''primal''). Such involutions sometimes have fixed points, so that the dual of is itself. For example, Desargues' theorem is self-dual in this sense under the ''standard duality in projective geometry''. In mathematical contexts, ''duality'' has numerous meanings. It has been described as "a very pervasive and important concept in (modern) mathematics" and "an important general theme that has manifestations in almost every area of mathematics". Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Of Sums
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form ( CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF), maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller). Minterms For a boolean function of n variables , a minterm is a product term in which each of the n variables appears ''exactly once'' (either in its complemented or uncomplemented form). Thus, a ''minterm'' is a logical expression of ''n'' variables that em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XOR Gate Based On 2-2 AOI Gate
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR ''excludes'' that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator J Translated as and by the infix operators XOR (, , or ), EOR, EXOR, \dot, \overline, \underline, , \oplus, \nleftrightarrow, and \not\equiv. Definition The truth table of A\nleftrightarrow B shows that it outputs true whenever the inputs differ: Equivalences, elimination, and introduction Exclusive disjunction essentially me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
