Logical NOR

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Logical NOR or NOR gate is a fundamental digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A NOR gate is a logic gate which gives a positive output only when both inputs are negative.

Operation

In essence, a NOR gate outputs true only when all inputs are false. Its output is false when any of the inputs are true. The symbol for the NOR operation is ↓, but it is more commonly represented by a plus sign inside a circle (+) when depicted in circuit diagrams. The NOR gate is a combination of an OR gate and a NOT gate. The output of the OR gate is fed into the NOT gate, resulting in the NOR functionality. The Boolean expression for a NOR gate is \( \overline{A + B} \), which can also be written as \( A \downarrow B \), where \( A \) and \( B \) are inputs.

Truth Table

The truth table for a 2-input NOR gate is as follows:

A	B	Output
0	0	1
0	1	0
1	0	0
1	1	0

This table shows that the output is only true (1) when both inputs A and B are false (0).

Symbol

The symbol for a NOR gate is a standard OR gate symbol with a circle (representing the NOT operation) at the output end. This circle is known as an inversion bubble and indicates that the logic of the gate is inverted.

Applications

NOR gates are widely used in electronic circuits and digital systems for performing various functions. They are particularly important because any other logic function (AND, OR, NOT, NAND, etc.) can be implemented using only NOR gates, making them universal gates. This property is crucial in the design of digital circuits, where minimizing the variety of gate types can simplify manufacturing and reduce costs.

NOR gates are used in the construction of flip-flops, which are basic building blocks for memory circuits, and in latches, which are essential for storing state information in digital systems. They are also employed in various logic circuits where a specific logic function needs to be performed.

Implementation

NOR gates can be implemented using different technologies, including TTL (Transistor-Transistor Logic), CMOS (Complementary Metal-Oxide-Semiconductor), and relay logic. Each technology has its advantages and disadvantages in terms of speed, power consumption, and cost.

See Also

• Logic gate
• OR gate
• NOT gate
• NAND gate
• Digital electronics