## Xnor Gate Truth Table

Contents

- 1 What are the rules of XNOR gate?
- 2 How do you write XOR in Boolean?
- 3 What is an example of a XNOR gate?
- 4 How is XNOR gate used in everyday life?
- 5 Why XOR and XNOR are not universal?
- 6 What is the advantage of XNOR gate?

## What are the rules of XNOR gate?

How does an XNOR Gate work? – The gate works by receiving two inputs, each designated with either a 1 or a 0. If both inputs are 0, the gate will produce a 1. If both inputs are 1, the gate will also produce a 1. However, if either input differs from the other, the gate will output a 0. Source

#### What is the Boolean expression for the XNOR gate?

Summary – A logic gate is one of the most basic switching circuits used in digital circuits to determine if an input pulse can pass through to the output. Logic gates are the building blocks of a digital circuit, and these perform various logical operations, which are necessary for any given digital circuit. Based on their operation, we have the following types of logic gates:

AND: The Boolean equation for AND gate is \(Y = A \cdot B\).OR: The Boolean expression for OR gate is: \(Y = A + B\).NOT: The Boolean expression for the NOT gate is: \(Y = \bar A\).NOR: The Boolean expression for the NOR gate is: \(Y = A + B\).NAND: The Boolean expression for the NAND gate is: \(Y = \overline \).XOR: the Boolean expression for the XOR gate is: \(Y = \bar A \cdot B + A \cdot \bar B\).XNOR: the Boolean expression for the XNOR gate is: \(Y = A \cdot B + \bar A\bar B\).

### What is the difference between XOR gate and XNOR gate?

Difference between XOR and XNOR –

XOR gate | XNOR gate |

It is known as odd detector | It is known as even detector |

It starts operating when one of the inputs are different | It starts operating when both of the inputs are same |

It is also known as the exclusive OR gate | It is also known as inclusive OR gate |

In the truth table, XOR gives a logical value of 1 when both the inputs are different. | In the truth table, XNOR gives a logical value of 1 when both the inputs are the same. |

In the symbolic representation of the XOR gate, there is no circle in front of the circuit symbol. | In the symbolic representation of the XNOR gate, there is a circle in front of the circuit symbol to indicate inversion or XOR gate. |

#### Is XNOR gate universal?

Alternatives – XNOR gate circuit using three mixed gates If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. A circuit implementing an XNOR function can be trivially constructed from an XOR gate followed by a NOT gate. If we consider the expression ( A + B ¯ ) ⋅ ( A ¯ + B ) })\cdot ( }+B)}, we can construct an XNOR gate circuit directly using AND, OR and NOT gates. However, this approach requires five gates of three different kinds. As alternative, if different gates are available we can apply to transform ( A + B ¯ ) ⋅ ( A ¯ + B ) ≡ ( A ⋅ B ) + ( A ¯ ⋅ B ¯ ) })\cdot ( }+B)\equiv (A\cdot B)+( }\cdot })} as stated above, and apply to the last term to get ( A ⋅ B ) + ( A + B ) ¯ }} which can be implemented using only three gates as shown on the right. An XNOR gate circuit can be made from four NOR gates. In fact, both NAND and NOR gates are so-called “universal gates” and any logical function can be constructed from either or alone.

Desired gate | NAND construction | NOR construction |
---|---|---|

An alternative arrangement is of five NAND gates in a topology that emphasizes the construction of the function from ( A ⋅ B ) + ( A ¯ ⋅ B ¯ ) }\cdot })}, noting from that a NAND gate is an inverted-input OR gate. Another alternative arrangement is of five NOR gates in a topology that emphasizes the construction of the function from ( A + B ¯ ) ⋅ ( A ¯ + B ) })\cdot ( }+B)}, noting from that a NOR gate is an inverted-input AND gate.

Desired gate | NAND construction | NOR construction |
---|---|---|

For the NAND constructions, the lower arrangement offers the advantage of a shorter propagation delay (the time delay between an input changing and the output changing). For the NOR constructions, the upper arrangement requires fewer gates. From the opposite perspective, constructing other gates using only XNOR gates is possible though XNOR is not a fully,

### Can XNOR gate have 3 inputs?

Logical expression – – Y=PQR ∴ Y=(PQ+PQ)R Three-input XNOR gate has three inputs, namely P, Q, and R, and one output, Y. The truth table is as follows –

P | Q | R | Y |

0 | 0 | 0 | 1 |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 0 | 0 | 0 |

1 | 0 | 1 | 1 |

1 | 1 | 0 | 1 |

1 | 1 | 1 | 0 |

Each input can have either a high(1) or low(0) state. Thus, there are eight(8) different combinations of three inputs. Therefore, we get eight(8) different outputs corresponding to the input combinations. Let us see the possible cases of input and output combination.

### Where is XNOR gate used?

Use of Ex-OR gate – Ex-NOR gates are used mainly in electronic circuits that perform arithmetic operations and data checking such as Adders, Subtractors or Parity Checkers, etc. As the Ex-NOR gate gives an output of logic level “1,” whenever its two inputs are equal, it can be used to compare the magnitude of two binary digits or numbers and so Ex-NOR gates are used in Digital Comparator circuits. Next Topic

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: XNOR Gate

#### Are XOR and XNOR equal?

For the second question, yes. XOR is true when there’s an odd number of 1s in the input. The output of an 2-input XOR is clearly defined. An XNOR is simply an XOR with an inverter after it.

### What are the laws of XOR and XNOR?

The Exclusive OR (XOR) gate gives logic 1 output if either, but not both, of its two inputs, are logic 1. The expression Y=A⊕B Y = A ⊕ B means XOR operation. The Exclusive NOR (XNOR) gate gives a logic 0 output if either, but not both, of its two inputs, are logic 1.

### What is the use of XOR and XNOR gate?

Common applications for XOR and XNOR gates are: comparators, switchable inverter/buffers, parity generator/checkers and adder/subtractor. They can also be used to simplify Boolean equations.

## How do you write XOR in Boolean?

Conditional logical OR operator || – The conditional logical OR operator ||, also known as the “short-circuiting” logical OR operator, computes the logical OR of its operands. The result of x || y is true if either x or y evaluates to true, Otherwise, the result is false,

- If x evaluates to true, y isn’t evaluated.
- In the following example, the right-hand operand of the || operator is a method call, which isn’t performed if the left-hand operand evaluates to true : bool SecondOperand() bool a = true || SecondOperand(); Console.WriteLine(a); // Output: // True bool b = false || SecondOperand(); Console.WriteLine(b); // Output: // Second operand is evaluated.

// True The logical OR operator | also computes the logical OR of its operands, but always evaluates both operands.

### What is XOR as a Boolean function?

More detail on the Group Theory – For those comfortable with the mathematics, here is a bit more detail of how XOR fits into group theory. An algebraic structure is simply a mathematical object (S, ~) comprising a set S and a binary operation ~ defined on the set. A group is an algebraic structure such that the following 4 properties hold:

~ is closed over X, i.e. the outcome of performing ~ is always an element of X ~ is associative An identity element e exists that, when combined with any other element of X, leaves it unchanged Every element in X has some inverse that, when combined with it, gives the identity element

We are interested in the operation XOR as applied to the set of Boolean vectors S = N, i.e. the set of vectors of length N whose entries can only take the values T and F. (I mean vector in the mathematical sense, i.e. it has fixed length. Do not confuse this with the C++ data structure std::vector, which has variable length.)We have already seen that XOR is associative, that the vector (F, F) is the identity element and that every element has itself as an inverse.

It’s easy to see that it is also closed over the set. Hence (S, XOR) is a group. In fact it is an Abelian group because we showed above that XOR is also commutative. Two groups are said to be isomorphic if there is a one-to-one mapping between the elements of the sets that preserves the operation. I won’t write that out formally (it’s easy enough to look up) or prove the isomorphisms below (let’s call that an exercise for the reader).

Instead I will just define them and state that they are isomorphisms. The group ( N, XOR) is isomorphic to the group ( N, +) of addition modulo 2 over the set of vectors whose elements are integers mod 2. The isomorphism simply maps T to 1 and F to 0.

The group ( N, XOR) is also isomorphic to the group (P(S), Δ) of symmetric difference Δ over the power set of N elements 3 : the isomorphism maps T to ‘included in the set’ and F to ‘excluded from the set’ for each of the N entries of the Boolean vector. Let’s take things one step further by considering a new algebraic structure called a ring,

A ring (S,+, ×) comprises a set S and a pair of binary operations + and × such that S is an Abelian group under + and a semigroup 4 under ×. Also × is distributive over +. The symbols + and × are chosen deliberately because these properties mean that the two operations behave like addition and multiplication.

We’ve already seen that XOR is an Abelian group over the set of Boolean vectors, so it can perform the role of the + operation in a ring. It turns out that AND fulfils the role of the * operation. Furthermore we can extend the isomorphisms above by mapping AND to multiplication modulo 2 and set intersection respectively.

Thus we have defined three isomorphic rings in the spaces of Boolean algebra, modulo arithmetic and set theory.

## What is an example of a XNOR gate?

Truth Table – XNOR gates commonly only have two inputs. It will only give out a HIGH or logic “1” if both its inputs are equal. So the inputs must both be HIGH or both be LOW for the output to become HIGH.

### Is XNOR gate commutative?

The Ex-NOR gate follows both associative and commutative properties.

#### Is XNOR the opposite of XOR?

Brief Description – XOR and XNOR are examples of logical operators having the truth-tables shown in Figure 1. Figure 1 Truth-tables for XOR and XNOR. The XOR function is only true if just one (and only one) of the input values is true, and false otherwise. XOR stands for eXclusive OR, As can be seen, the output values of XNOR are simply the inverse of the corresponding output values of XOR.

## How is XNOR gate used in everyday life?

Ex-NOR gate applications –

The XNOR logic gates are used in error detecting circuits which are to detect Odd parity or even parity bits in digital data transmission circuits. XNOR gate is mainly used in arithmetic and encryption circuits. This process is the combinational operation of the XOR and XNOR gates, by using 6 transistors for low power application.

This is also used as Heat exchanger tank, which will ring the alarm when the water temperature level goes up or down, to the pre-set level. The Heat exchanger circuit is explained below.

## Why XOR and XNOR are not universal?

Exercise : Digital Electronics – Section 4 46. Assertion (A): XOR gate is not universal gate. Reason (R): It is not possible to realize any Boolean function using XOR gates only. Both A and R are correct and R is correct explanation of A Both A and R are correct but R is not correct explanation of A Explanation: A universal gate is one which can be used to realize any Boolean function using that type of gates only. where d is Resolution in volts. Resolution in volts = volts per step = 0.01V 0r 10mV. 49. The number of bits in EBCDIC is Explanation: EBCDIC is an 8 bit code.

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#### How many NAND gates are used in XNOR gate?

Implementation of XNOR Gate from NAND Gate – As discussed above, the NAND gate is a universal logic, using which we can implement any other type of logic gate. The realization of XNOR gate using NAND gates is shown in Figure-3. From the logic circuit diagram of the XNOR gate using NAND gates only, it is clear that we require 5 NAND gates. Now, let us understand how this NAND logic circuit functions to produce an output equivalent to the XNOR gate- The output of the first NAND gate is, $$\mathrm }$$ The outputs of the secondary and third NAND gates are, $$\mathrm }}$$ $$\mathrm }}$$ These two outputs (Y2 and Y3) are connected to the fourth NAND gate.

This NAND gate will produce an output which is, $$\mathrm }\cdot\overline }}}$$ $$\mathrm +B\cdot\overline =A(\bar +\bar )+B(\bar +\bar )}$$ $$\mathrm +A\bar +\bar B+B\bar }$$ $$\mathrm +\bar B=A\bigoplus B}$$ Finally, the output of the fourth NAND gate is input to the fifth NAND gate that functions as an inverter, and produces an output equivalent to the XNOR gate, i.e., $$\mathrm =A\bigodot B}$$ This is the output of the XNOR gate.

Therefore, in this way, we can implement the XNOR gate from NAND gates only.

## What is the advantage of XNOR gate?

Applications of the XNOR Gates – XNOR gates are mostly employed in the electronic circuits that conduct data checking and arithmetic operations, such as Subtractions, adders, and Parity Checkers, among other things. X-NOR gates are employed in Digital Comparator circuits because they produce a logic level “1” output when their two inputs are equal.

### What is another name for the XNOR gate?

Truth table for an XNOR gateInput A | Input B | Output |
---|---|---|

false | false | true |

false | true | false |

true | false | false |

true | true | true |

An XNOR gate (sometimes referred to by its extended name, Exclusive NOR gate) is a digital logic gate with two or more inputs and one output that performs logical equality, The output of an XNOR gate is true when all of its inputs are true or when all of its inputs are false,

#### How many transistors are in XNOR gate?

XOR and XNOR The Exclusive OR (or XOR) relationship $F = A\oplus B$ is defined by the truth tables shown in Fig.1 and the equivalent two-variable logic expressions $F_ =A\cdot \overline + \overline \cdot B$ and $F_ = (A+B)\cdot (\overline + \overline )$.

The XOR function is frequently used in digital circuits to manipulate signals that represent binary numbers—these circuits will be presented in a later module. For now, note the XOR output is asserted whenever an odd number of inputs are asserted. This “odd detector” nature of the XOR relationship holds for any number of inputs.

Compound XOR functions like $F = A \oplus(B\cdot C)$ can always be written in an equivalent SOP or POS forms: $F_ =A\cdot \overline + \overline \cdot (B\cdot C)$ and $F_ = (A+B\cdot C)\cdot (\overline + \overline )$ The XNOR function is the inverse of the XOR function.

Since the output of a 2-input XNOR is asserted when both inputs are the same, it is sometimes referred to as the Equivalence function (EQV), but this name is misleading because it does not hold for three or more variables (i.e., the output of a 3-input XNOR is not asserted whenever all three inputs are the same).

Truth tables for 2 and 3 input XNOR functions are shown in Fig.2, and it can be seen that for each combination of inputs, the output is the inverse of the XOR truth tables above. The Exclusive NOR (or XNOR) relationship $F = \overline $ shown in the truth tables has the equivalent two-variable logic expressions: $F_ =\overline \cdot \overline + A\cdot B$ and $F_ = (\overline +B)\cdot (A + \overline )$ If either the A or B inputs are in the XNOR truth table inverted, then XOR outputs are produced; that is, $F = \overline $ produces the same logic output as $F = \overline \oplus B$ or $F = A \oplus \overline $.

If both the A and B inputs are inverted, XNOR outputs are still produced: $F = \overline $ produces the same output as $F = \overline \oplus \overline }$. This same property holds for the XOR function—inverting any single input variable will result in XNOR function, and inverting two inputs will again produce the XOR function.

In fact, this property can be generalized to XOR/XNOR functions of any number of inputs: any single input inversion changes the function output between the XOR and XNOR functions; any two input signal inversions does not change function outputs; any three input signal inversions changes the function output between the XOR and XNOR functions, etc.

- More succinctly, inverting an odd number of inputs changes an XOR to an XNOR and vice-versa, inverting an even number of inputs changes nothing, and inverting the entire function has the same effect as inverting a single input.
- Some representative cases are shown.
- Begin F=\overline &\iff F=\overline \oplus B\oplus C &\iff F=\overline \oplus \overline \oplus \overline \\ F=A\oplus B\oplus C & \iff F=\overline \oplus \overline \oplus C &\iff F=\overline \oplus C} \end $$ An even more succinct description of the XOR and XNOR function outputs can be drawn from the properties discussed.

The XOR output is asserted whenever an odd number of inputs are asserted, and the XNOR is asserted whenever an even number of inputs are asserted: the XOR is an odd detector, and the XNOR an even detector. This very useful property will be exploited in data error detection circuits discussed later.

- XOR and XNOR gate symbols are shown below in Fig.3.
- CMOS circuits for either function can be can built from just 6 transistors, but those circuits have some undesirable features.
- More typically, XOR and XNOR logic gates are built from three NAND gates and two inverters, and so take 16 transistors.
- A useful application of the XOR function is the “controlled inverter” circuit illustrated below in Fig.4.

The truth table, derived directly from the XOR truth table, uses an XOR gate with one input tied to a signal named “control”. When control is a ‘1’ the input A is inverted, but when control is a ‘0’ A is simply passed through the logic gate without modification.

#### Where is XNOR gate used?

Use of Ex-OR gate – Ex-NOR gates are used mainly in electronic circuits that perform arithmetic operations and data checking such as Adders, Subtractors or Parity Checkers, etc. As the Ex-NOR gate gives an output of logic level “1,” whenever its two inputs are equal, it can be used to compare the magnitude of two binary digits or numbers and so Ex-NOR gates are used in Digital Comparator circuits. Next Topic

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: XNOR Gate

### What does XOR and XNOR mean?

XOR and XNOR The Exclusive OR (or XOR) relationship $F = A\oplus B$ is defined by the truth tables shown in Fig.1 and the equivalent two-variable logic expressions $F_ =A\cdot \overline + \overline \cdot B$ and $F_ = (A+B)\cdot (\overline + \overline )$.

The XOR function is frequently used in digital circuits to manipulate signals that represent binary numbers—these circuits will be presented in a later module. For now, note the XOR output is asserted whenever an odd number of inputs are asserted. This “odd detector” nature of the XOR relationship holds for any number of inputs.

Compound XOR functions like $F = A \oplus(B\cdot C)$ can always be written in an equivalent SOP or POS forms: $F_ =A\cdot \overline + \overline \cdot (B\cdot C)$ and $F_ = (A+B\cdot C)\cdot (\overline + \overline )$ The XNOR function is the inverse of the XOR function.

Since the output of a 2-input XNOR is asserted when both inputs are the same, it is sometimes referred to as the Equivalence function (EQV), but this name is misleading because it does not hold for three or more variables (i.e., the output of a 3-input XNOR is not asserted whenever all three inputs are the same).

Truth tables for 2 and 3 input XNOR functions are shown in Fig.2, and it can be seen that for each combination of inputs, the output is the inverse of the XOR truth tables above. The Exclusive NOR (or XNOR) relationship $F = \overline $ shown in the truth tables has the equivalent two-variable logic expressions: $F_ =\overline \cdot \overline + A\cdot B$ and $F_ = (\overline +B)\cdot (A + \overline )$ If either the A or B inputs are in the XNOR truth table inverted, then XOR outputs are produced; that is, $F = \overline $ produces the same logic output as $F = \overline \oplus B$ or $F = A \oplus \overline $.

- If both the A and B inputs are inverted, XNOR outputs are still produced: $F = \overline $ produces the same output as $F = \overline \oplus \overline }$.
- This same property holds for the XOR function—inverting any single input variable will result in XNOR function, and inverting two inputs will again produce the XOR function.

In fact, this property can be generalized to XOR/XNOR functions of any number of inputs: any single input inversion changes the function output between the XOR and XNOR functions; any two input signal inversions does not change function outputs; any three input signal inversions changes the function output between the XOR and XNOR functions, etc.

- More succinctly, inverting an odd number of inputs changes an XOR to an XNOR and vice-versa, inverting an even number of inputs changes nothing, and inverting the entire function has the same effect as inverting a single input.
- Some representative cases are shown.
- Begin F=\overline &\iff F=\overline \oplus B\oplus C &\iff F=\overline \oplus \overline \oplus \overline \\ F=A\oplus B\oplus C & \iff F=\overline \oplus \overline \oplus C &\iff F=\overline \oplus C} \end $$ An even more succinct description of the XOR and XNOR function outputs can be drawn from the properties discussed.

The XOR output is asserted whenever an odd number of inputs are asserted, and the XNOR is asserted whenever an even number of inputs are asserted: the XOR is an odd detector, and the XNOR an even detector. This very useful property will be exploited in data error detection circuits discussed later.

- XOR and XNOR gate symbols are shown below in Fig.3.
- CMOS circuits for either function can be can built from just 6 transistors, but those circuits have some undesirable features.
- More typically, XOR and XNOR logic gates are built from three NAND gates and two inverters, and so take 16 transistors.
- A useful application of the XOR function is the “controlled inverter” circuit illustrated below in Fig.4.

The truth table, derived directly from the XOR truth table, uses an XOR gate with one input tied to a signal named “control”. When control is a ‘1’ the input A is inverted, but when control is a ‘0’ A is simply passed through the logic gate without modification.

### What is logic gates with truth table?

Summary of 2-input Logic Gates – The following Boolean ALgebra Truth Tables compare the logical functions of the 2-input logic gates above.

Inputs | Truth Table Outputs For Each Gate | ||||||

A | B | AND | NAND | OR | NOR | EX-OR | EX-NOR |

1 | 1 | 1 | |||||

1 | 1 | 1 | 1 | ||||

1 | 1 | 1 | 1 | ||||

1 | 1 | 1 | 1 | 1 |

The following Boolean Algebra truth tables gives a list of the common logic functions and their equivalent Boolean notation.

Logic Function | Boolean Notation |

AND | A.B |

OR | A+B |

NOT | A |

NAND | A,B |

NOR | A+B |

EX-OR | (A. B ) + ( A,B) or A ⊕ B |

EX-NOR | (A.B) + ( A, B ) or A ⊕ B |

2-input logic gate truth tables are given here as examples of the operation of each logic function, but there are many more logic gates with 3, 4 even 8 individual inputs. The multiple input gates are no different to the simple 2-input gates above, So a 4-input AND gate would still require ALL 4-inputs to be present to produce the required output at Q and its larger truth table would reflect that.