This 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 22=4 possible combinations of inputs. The output level is high when both inputs are set to a different logic level. The Boolean expression of 2-input 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
Unlike the 2-input XOR gate, the 3-input XOR gate has three inputs. There are 23 = 8 possible combinations of inputs. The Boolean expression of the logical Ex-OR 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
We can form the XOR or Ex-OR 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 Ex-OR gate also. This is an easier way of producing Ex-OR gate functionality.
The Ex-or gate plays an important role in constructing digital circuits that perform arithmetic operations and calculations. Especially Adders and Half-Adders, as they can provide a "carry-bit" 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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