Question

Give the three representations of a NOR gate and say in words what NOR means.

Short answer

NOR outputs true only if both inputs are false; it's expressed as Q = \(\overline{A + B}\).

Step-by-step solution

Understanding the NOR Gate

A NOR gate is a digital logic gate that outputs true or 1 only when both inputs are false or 0. It is the complement of the OR gate.

Truth Table Representation

Construct the truth table for a NOR gate, which has two inputs, A and B, and one output, Q. | A | B | Q (A NOR B) | |---|---|------------| | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 0 | This table shows that the output Q is only 1 when both A and B are 0.

Symbol Representation

The NOR gate symbol is similar to the OR gate, but with a small circle (an inverter) on the output. This circle indicates that the output is inverted compared to the OR gate.

Boolean Expression Representation

The Boolean expression for a NOR gate is \[ Q = \overline{A + B} \]This indicates that the output Q is the negation of the OR operation between inputs A and B.

Key concepts

Digital Logic

Digital logic is a fundamental concept used in electronics, commonly involved in designing circuits and systems. It revolves around binary numbers, which are either 0 or 1. These numbers correspond to different voltage levels, where 0 usually represents a low voltage and 1 represents a high voltage.
This is how computers process information.
Digital logic is primarily used to combine and manipulate these binary states with the help of various logic gates such as AND, OR, NOT, and of course, the NOR gate. Each gate is designed to perform a specific logical operation, using special symbols for representation.

• AND Gate: Outputs true only if both inputs are true.
• OR Gate: Outputs true if at least one input is true.
• NOR Gate: Outputs true only when all inputs are false.
• NOT Gate: Inverts the input signal.

The application of digital logic allows electronic devices to perform complex operations simply by combining these basic gates. It's like building a complex machine from simple building blocks.

Truth Table

A truth table is a basic tool used in digital logic to show how a logic gate responds to various combinations of inputs.
It's essentially a structured list that displays all possible input states and their corresponding output states. In the context of a NOR gate, the truth table is particularly simple yet powerful. For example, consider a NOR gate with two inputs, A and B:

• When both inputs are low (0), the output is high (1). This is the only time the output is high.
• If either or both inputs are high (1), the output is low (0).

By reviewing a truth table, it becomes evident how a NOR gate functions differently compared to other gates. It offers an intuitive way to predict the behavior of more complex circuits by understanding their basic building blocks. This is essential for designing and troubleshooting digital systems.

Boolean Expression

In digital logic, Boolean expressions are used to mathematically model the function of logic gates.
These expressions are essential for understanding how a logical operation transforms its inputs.For a NOR gate, the Boolean expression is written as:\[Q = \overline{A + B}\]This expression signifies that the output \(Q\) is the inverse of the OR operation between inputs \(A\) and \(B\).
The plus sign \(+\) symbolizes the OR operation, while the line over the expression represents negation, indicating that the OR output is inverted.Understanding Boolean expressions allows people to convey the behavior of logic gates using mathematical notation, which is especially useful in digital circuit design and analysis. Boolean algebra helps simplify complex logic circuits to make them more efficient.

Inverter

An inverter, also known as a NOT gate, is another fundamental component in digital logic.
Its main function is to invert the input signal—converting a 0 to a 1, and a 1 to a 0. The inverter is visually represented in circuit diagrams by a triangle pointing to a small circle.
In the case of a NOR gate, this inverter plays a significant role. The NOR gate is essentially an OR gate followed by an inverter. This is why the NOR gate's symbol includes an extra circle at the output; it signifies that the OR operation's result is negated. This inverter effectively alters the behavior of the OR gate to perform a NOR operation, which produces a true output only when all its inputs are false. Inverters are critical in digital systems as they allow flexibility by enabling the opposite operation of a given logic signal, thus broadening the variety of possible functions and applications in electronics.