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XNOR
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR ( XOR) gate. It is equivalent to the logical connective (\leftrightarrow) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results. The algebraic notation used to represent the XNOR operation is S = A \odot B. The algebraic expressions (A + \overline) \cdot (\overline + B) and A \cdot B + \overline A \cdot \overline B both represent the XNOR gate with inputs ''A'' and ''B''. Symbols There are two symbols for XNOR gates: one with distinctive shape and one with rectangular shape and label. Both symbols f ... [...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-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] |
XNOR From NOR 2
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. It is equivalent to the logical connective (\leftrightarrow) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results. The algebraic notation used to represent the XNOR operation is S = A \odot B. The algebraic expressions (A + \overline) \cdot (\overline + B) and A \cdot B + \overline A \cdot \overline B both represent the XNOR gate with inputs ''A'' and ''B''. Symbols There are two symbols for XNOR gates: one with distinctive shape and one with rectangular shape and label. Both symbols fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XNOR From NOR
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR gate, XOR) gate. It is equivalent to the logical connective (\leftrightarrow) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results. The Boolean algebra, algebraic notation used to represent the XNOR operation is S = A \odot B. The algebraic expressions (A + \overline) \cdot (\overline + B) and A \cdot B + \overline A \cdot \overline B both represent the XNOR gate with inputs ''A'' and ''B''. Symbols There are logic gate#Symbols, two symbols for XNOR gates: one with distinctive shape and one with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XNOR From NAND
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. It is equivalent to the logical connective (\leftrightarrow) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results. The algebraic notation used to represent the XNOR operation is S = A \odot B. The algebraic expressions (A + \overline) \cdot (\overline + B) and A \cdot B + \overline A \cdot \overline B both represent the XNOR gate with inputs ''A'' and ''B''. Symbols There are two symbols for XNOR gates: one with distinctive shape and one with rectangular shape and label. Both symbols fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NOR Logic
A NOR gate or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative. Like NAND gates, NOR gates are so-called " universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, the Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, integrated circuits are not constructed exclusively from a single type of gate. Instead, EDA tools are used to convert the description of a logical circuit to a netlist of complex gates ( standard cells) or transistors ( full custom approach). NOR A NOR gate is logically an inverted OR gate. It has the following truth table: Making other gates by using NOR gates A NOR gate is a universal gate, meaning that any other gate can be represented as a combination of NOR gates. NOT This is made by joining the inputs of a NOR gate. As a NOR gate is equivalent to an OR gate leading to NOT gate, joini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAND Logic
The NAND Boolean function has the property of functional completeness. This means that any Boolean expression can be re-expressed by an equivalent expression utilizing only NAND operations. For example, the function NOT(x) may be equivalently expressed as NAND(x,x). In the field of digital electronic circuits, this implies that it is possible to implement any Boolean function using just NAND gates. The mathematical proof for this was published by Henry M. Sheffer in 1913 in the ''Transactions of the American Mathematical Society'' (Sheffer 1913). A similar case applies to the NOR function, and this is referred to as NOR logic. NAND A NAND gate is an inverted AND gate. It has the following truth table: In CMOS logic, if both of the A and B inputs are high, then both the NMOS transistors (bottom half of the diagram) will conduct, neither of the PMOS transistors (top half) will conduct, and a conductive path will be established between the output and Vss (ground), bringin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Morgan's Law
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: * The negation of "A and B" is the same as "not A or not B". * The negation of "A or B" is the same as "not A and not B". or * The complement of the union of two sets is the same as the intersection of their complements * The complement of the intersection of two sets is the same as the union of their complements or * not (A or B) = (not A) and (not B) * not (A and B) = (not A) or (not B) where "A or B" is an " inclusive or" meaning ''at least'' one of A or B rather than an "exclusive or" that means ''exactly'' one of A or B. Another form of De Morgan's law is the following as see ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3 Gate XNOR
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the Caliphate in the 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
