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XNOR Gate

Delve into the intricacies of the XNOR Gate, a fundamental concept in Computer Science. Understanding the XNOR Gate is key to grasping more complex digital logic and circuit designs. In this detailed study, you'll explore its definition, operation, boolean expressions, and truth table. The article also offers insights into the functionality of a 3 input XNOR Gate and its practical examples. Enhance your knowledge and explore the world of Computer Science with clarity and precision.

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Jetzt kostenlos anmeldenDelve into the intricacies of the XNOR Gate, a fundamental concept in Computer Science. Understanding the XNOR Gate is key to grasping more complex digital logic and circuit designs. In this detailed study, you'll explore its definition, operation, boolean expressions, and truth table. The article also offers insights into the functionality of a 3 input XNOR Gate and its practical examples. Enhance your knowledge and explore the world of Computer Science with clarity and precision.

In the field of Computer Science and DIGITAL LOGIC, one of the most common components you will encounter is the XNOR gate, also known as 'equivalence gate'.

An XNOR gate (denoted as XNOR) is a digital logic gate that outputs true or '1' only when the number of true inputs is even. This peculiar ability makes it essential in certain circuits. The name "XNOR" is a portmanteau of XOR (which signifies 'exclusive OR') and NOT, reflecting the fact that its output is the inverse or 'NOT' of that of an XOR gate.

- \( A' \) represents NOT A
- \( B' \) represents NOT B
- \( + \) is the Boolean OR operation

A | B | Output (O) |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

if(A == B): output = 1 else: output = 0

Despite appearing similar to the XOR gate, the XNOR gate holds its own unique place in computer science and digital logic design. It is essential in circuits needing parity checking and equal detection functionality.

A | B | Output (O) |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

- \( AB \) stands for A AND B, meaning both A and B are 1
- \( A'B' \) means A NOR B, meaning both A and B are 0
- The '+' in between represents the OR operation

if(A == B): output = 1 else: output = 0This segment provides a deep understanding of the functions of an XNOR gate, from its practical applications to Boolean expression. Regardless of how advanced the digital circuit is, this very logic forms the core of digital operations and computing.

Input A | Input B | Output O |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

Input A | Input B | Input C | Output O |

0 | 0 | 0 | 1 |

0 | 0 | 1 | 0 |

0 | 1 | 1 | 1 |

1 | 1 | 1 | 1 |

Array = [TRUE, FALSE, TRUE, TRUE, FALSE] counter = 0 for i in Array: if(i): counter+=1 if(counter % 2 == 0): output = TRUE else: output = FALSEThis operation essentially works as an XNOR gate over the array of boolean values, illustrating a unique and practical application of the XNOR gate concept.

- The XNOR gate is a fundamental concept in Computer Science and digital logic, also known as 'equivalence gate'.
- An XNOR gate outputs true or '1' only when the number of true inputs is even, its output is the inverse of an XOR gate.
- The operation of an XNOR gate can be described by the Boolean expression \( A' B + AB' \), expressing the combination of NOT, AND and OR operations.
- The XNOR gate's truth table makes clear that the output is 'true' or '1' only when both inputs are the same, hence the term 'equivalence gate'.
- A 3 input XNOR Gate yields a high output ('1') when the number of high inputs is even, while practical examples of XNOR gates can be found in parity generators and checkers, and unary operations in digital applications.

An XNOR gate, in computer science, is a gate that outputs true or '1' only when the number of true inputs is even. This is used in digital electronics to carry out logical equality, essentially determining if the number of true inputs matches the expected values.

An XNOR gate, in a digital logic circuit, operates by producing an output that's true or '1' only when the number of true inputs is even. In a two-input gate, the output is true if both inputs are the same (either both true or both false).

The truth table of an XNOR gate is: 0 XNOR 0 = 1, 0 XNOR 1 = 0, 1 XNOR 0 = 0, 1 XNOR 1 = 1. The Boolean expression for XNOR is A' B + A B', where A and B are inputs.

The main difference between XOR and XNOR gates in computing logic is their output. An XOR gate produces a high output (1) if the number of high inputs (1s) is odd. On the other hand, an XNOR gate produces a high output (1) if the number of high inputs (1s) is even.

An XNOR gate can be constructed with a combination of AND, OR, and NOT gates. For two inputs (A and B), you would use two NOT gates for the individual inputs, two AND gates for the combination of original and negated inputs, and then an OR gate combining the outputs of the AND gates.

What is an XNOR gate in digital logic?

An XNOR gate is a digital logic gate that outputs true or '1' only when the number of true inputs is even. Its name reflects that its output is the inverse or 'NOT' of that of an XOR gate.

What is the Boolean expression for the operation of the XNOR gate?

The Boolean expression for the operation of the XNOR gate is \( A' B + AB' \), where \( A' \) represents NOT A, \( B' \) represents NOT B, and \( + \) is the Boolean OR operation.

When does an XNOR gate output '1' or true?

An XNOR gate outputs '1' or true only when both inputs are the same, whether they are 0 or 1.

What is the other name for the XNOR gate and why?

The XNOR gate is also often referred to as the 'equivalence gate' because it outputs '1' or true when both inputs are the same.

What is the boolean expression for the XNOR gate operation and what does it represent?

The boolean expression for the XNOR gate is AB + A'B'. This implies that the output is '1' when either both A and B are true or when both A and B are false.

What does the XNOR gate output when the number of true inputs is even?

The XNOR gate outputs 'true' or '1' only when the number of true inputs is even.

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