![]() Symbol and truth table for NAND gate What are NAND gates used for? The Boolean expression for a NAND gate with two inputs (A, B) and output X is:įigure 1. The symbol and truth table for a NAND gate is shown in Figure 1. While an AND gate outputs a logical “1” only if both inputs are logical “1,” a NAND gate outputs a logical “0” for this same combination of inputs. XOR gates and AND gates are the two most-used structures in VLSI applications.NAND is an abbreviation for “NOT AND.” A two-input NAND gate is a digital combination logic circuit that performs the logical inverse of an AND gate. Applications Example half adder circuit diagram Example full adder circuit diagram This makes it practically useful as a parity generator or a modulo-2 adder.įor example, the 74LVC1G386 microchip is advertised as a three-input logic gate, and implements a parity generator. The result is a circuit that outputs a 1 when the number of 1s at its inputs is odd, and a 0 when the number of incoming 1s is even. It is most common to regard subsequent inputs as being applied through a cascade of binary exclusive-or operations: the first two signals are fed into an XOR gate, then the output of that gate is fed into a second XOR gate together with the third signal, and so on for any remaining signals. However, it is rarely implemented this way in practice. If a logic gate were to accept three or more inputs and produce a true output if exactly one of those inputs were true, then it would in effect be a one-hot detector (and indeed this is the case for only two inputs). Literal interpretation of the name "exclusive or", or observation of the IEC rectangular symbol, raises the question of correct behaviour with additional inputs. Standard chip packages Philips 4070 quad dual input XOR chip on printed circuit board For the NOR constructions, the lower arrangement offers the advantage of a shorter propagation delay (the time delay between an input changing and the output changing). The algebraic expressions A ⋅ B ¯ + A ¯ ⋅ B A\cdot, noting from de Morgan's Law that a NAND gate is an inverted-input OR gate.įor the NAND constructions, the upper arrangement requires fewer gates. The gate is also used in subtractors and comparators. A half adder consists of an XOR gate and an AND gate. As a result, XOR gates are used to implement binary addition in computers. XOR can also be viewed as addition modulo 2. Hence it functions as a inverter (a NOT gate) which may be activated or deactivated by a switch. A way to remember XOR is "must have one or the other but not both".Īn 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. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. If both inputs are false (0/LOW) or both are true, a false output results. An XOR gate implements an 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. 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. For other uses, see XOR (disambiguation). ![]() For XOR logical operation, see Exclusive or. This article is about XOR digital logic gate (e.g.
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