XOR Logic Gate using Other Logic Gate

Dec 6 • General • 1895 Views • No Comments on XOR Logic Gate using Other Logic Gate

The XOR gate is a digital logic gate. It is implemented as an Exclusive OR gate in which a true output (1) is received as the resultant output if one of the inputs to the logic gate is true (1). Otherwise either if both the inputs are false (0) or if both are true (1) then a false output (0) is received as a resultant. So this behavior of the gate which is summarized in the truth table shown below. It performs exclusive disjunction. A simple way to remember the truth table of  XOR gate is “One or the other but not both“.

XOR gate represents the inequality function in which the output is HIGH (1) if the inputs are not alike otherwise the output is LOW (0) if not alike. The XOR gate can also be viewed as an addition modulo 2. As a result, the XOR gates are used to implement the binary addition in computers. A half adder consists of an XOR gate and an AND Gate.

If a specific type of gate is not available, then a circuit that implements the same function can be constructed from the other available gates also. Like for example a circuit implementing an XOR function can be trivially constructed from an XNOR gate which is followed by a NOT gate. So if we consider the expression A \cdot \overline{B} + \overline{A} \cdot B, we can construct an XOR logic gate circuit directly using AND, OR and NOT logic gates. However, this approach requires five gates of three different kinds.

An XOR logic gate circuit can be made from four NAND or five NOR logic gates as in the configurations shown below. In fact, both the NAND logic gates and NOR logic gates are also called “universal gates” and any logical function can be constructed from either of the NAND logic gate or NOR logic gate.

For XOR logic gate Truth table:

Input

output

A

B

Q

Q’

0

0

0

1

0

1

1

0

1

0

1

0

1

1

0

1

XOR logic gate application:

The XOR logic gate can be used as a one – bit adder. This is the main principle in the half adder and the combined AND – XOR circuit may be chained together in order to add ever longer binary numbers.

XOR logic gate Using NAND logic gate:

XOR Logic Gate using NAND Logic Gate

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