XOR gateThe XOR gate stands for the ExclusiveOR gate. This gate is a special type of gate used in different types of computational circuits. Apart from the AND, OR, NOT, NAND, and NOR gate, there are two special gates, i.e., ExOR and ExNOR. These gates are not basic gates in their own and are constructed by combining with other logic gates. Their Boolean output function is significant enough to be considered as a complete logic gate. The XOR and XNOR gates are the hybrids gates. The 2input OR gate is also known as the InclusiveOR gate because when both inputs A and B are set to 1, the output comes out 1(high). In the ExOR function, the logic output "1" is obtained only when either A="1" or B="1" but not both together at the same time. Simply, the output of the XOR gate is high(1) only when both the inputs are different from each other. The plus(+) sign within the circle is used as the Boolean expression of the XOR gate. So, the symbol of the XOR gate is ⨁. This ExOR symbol also defines the "direct sum of subobjects" expression. These are the following types of ExclusiveOR gate: 2input ExOR gateThis is a simple form of the hybrid gate XOR. In this type of XOR gate, there are only two input values and an output value. There are 2^{2}=4 possible combinations of inputs. The output level is high when both inputs are set to a different logic level. The Boolean expression of 2input XOR gate is as follows:
Y=(A⨁B)
Y=(A' B+AB') The truth table and logic design are given below: Logic Design Truth Table
The 3input XOR GateUnlike the 2input XOR gate, the 3input XOR gate has three inputs. There are 2^{3}=8 possible combinations of inputs. The Boolean expression of the logical ExOR gate is as follows:
Y=A⨁B⨁C
Y=A(BC)'+A' BC'+(AB)' C+ABC The truth table and logic design are given below: Logic Design Truth Table
ExOR gate equivalent circuitWe can form the XOR or ExOR gate using gates such as AND, OR, and a universal gate NAND. The main disadvantage of this implementation is that we need to use different types of gates to form a single XOR gate. By using only the NAND gate, we can implement the ExOR gate also. This is an easier way of producing ExOR gate functionality. Use of ExOR gateThe Exor gate plays an important role in constructing digital circuits that perform arithmetic operations and calculations. Especially Adders and HalfAdders, as they can provide a "carrybit" function or as a controlled inverter, where one input passes the binary data, and the other input is supplied with a control signal.
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