Logical Behavior of an OR Gate

An OR gate outputs \(\mathsf{1}\) when any input is \(\mathsf{1}\). In the only remaining case (when all inputs are \(\mathsf{0}\)), the output is \(\mathsf{0}\). An OR gate has a minimum of \(\mathsf{2}\) inputs and \(\mathsf{1}\) output signal.

Representation of an OR Gate

In this section, we will explore the symbolic and mathematical representations commonly associated with the gate. Additionally, we will examine how the gate is modeled using Verilog HDL.

Symbolic Representation

The symbolic representation of all the logic gates may vary depending on regional or institutional standards. In the United States, the American National Standards Institute (ANSI) and the Military Standard (MIL-STD-806B) standardized a symbol while European organizations such as the International Electrotechnical Commission (IEC), particularly in IEC 60617, favor a rectangular symbol. The Institute of Electrical and Electronics Engineers (IEEE), through standards like IEEE Std 91-1984, closely aligns with ANSI conventions and plays a pivotal role in harmonizing gate symbols across international platforms. Other countries and standards bodies may adopt slight variations to meet local engineering norms, but the underlying function always remains universally understood.

American Symbol

The OR gate is commonly illustrated as a concave-tipped figure, resembling a curved shield. On the left side, two or more input signals converge toward its slightly tapered edge, symbolizing the logical inclusion of multiple possibilities. The right side expands smoothly into a broad arc, from which the output signal emerges—activated when any of the input lines carry a high (true) value. This visual representation echoes the gate’s inclusive nature: if at least one input is active, the gate ensures that the signal flows onward.

European Symbol

In European engineering documentation, the OR gate is depicted as a rectangular block, maintaining a consistent layout for schematic clarity. Input lines enter from the left side, converging into the gate, while a single output line exits from the right, signifying the result of the logical operation. To indicate its function, the interior of the rectangle is marked with the symbol “≥1”, denoting that the gate activates its output when one or more of the input lines carry a high (true) signal. This minimalist representation streamlines complex circuit designs while preserving clear logic annotation.

IEEE Symbol

The gate’s visual representation aligns with the American ANSI style, most notably illustrated through the characteristic curved symbol, but just like the AND symbol, is slightly longer than its ANSI counterpart.

Mathematical Representation

To represent the operation of an OR gate mathematically, we commonly use the plus symbol \(\mathsf{+}\), analogous to addition in algebra. For example, the expression \(\mathsf{A+B}\) indicates that any of the inputs, \(\mathsf{A}\) and \(\mathsf{B}\), must be true (or high) for the output to be true—mirroring the logical OR operation. If \(\mathsf{A}\) and \(\mathsf{B}\) are two input signals and their OR produces the output signal \(\mathsf{OUT}\), it can be written as:

\[\mathsf{OUT= A+B} \]

If another input \(\mathsf{C}\) is added, then:

\[\mathsf{OUT= A+B+C} \]

Verilog HDL Representation

In Verilog HDL, the | symbol is used to represent the OR operation, formerly called the Bitwise OR operation at the dataflow and higher abstraction levels. At the gate level, the OR gate is instantiated using the keyword or(<output>, <inputs>). Given two input signals, A and B, the OR gate produces an output signal OUT using the following logic (only the relevant code is shown).

assign OUT = A | B; // dataflow coding
or o1 (OUT, A, B); //gate-level coding

If another input \(\mathsf{C}\) is added, then:

assign OUT = A | B | C; // dataflow coding
or o2 (OUT, A, B, C); //gate-level coding

Truth Table of an OR Gate

A truth table is a structured way to show the output of a logical operation or digital circuit for every possible combination of input values. It’s a staple tool in boolean algebra, digital electronics, and computer science, especially when designing or analyzing logic gates and circuits.

A truth table, typically has input columns to the left, and to the right are the derived or output expressions. Each row in a truth table represents a unque set of input combination.

Truth tables for 2-, 3-, and 4-input OR gates are shown here.

Truth Table of a 2-Input OR Gate

The following truth table demonstrates the behavior of a basic 2-input OR gate, where the inputs are labeled \(\mathsf{A}\) and\(\mathsf{B}\), and the resulting output is represented as \(\mathsf{OR}\). This gate yields a high output (\(\mathsf{1}\)) when any of the inputs is high; otherwise, the output remains low (\(\mathsf{0}\)). The table captures every possible combination of inputs along with their corresponding output values. The truth table is presented after the OR gate symbol that corresponds with the truth table.

Truth Table of a 3-Input OR Gate

The following truth table demonstrates the behavior of a basic 3-input OR gate, where the inputs are labeled \(\mathsf{A}\), \(\mathsf{B}\) and \(\mathsf{C}\), and the resulting output is represented as \(\mathsf{OR}\). This gate yields a high output (\(\mathsf{1}\)) when any of the inputs is high; otherwise, the output remains low (\(\mathsf{0}\)). The table captures every possible combination of inputs along with their corresponding output values. The truth table is presented after the OR gate symbol that corresponds with the truth table.

Truth Table of a 4-Input OR Gate

The following truth table demonstrates the behavior of a basic 4-input OR gate, where the inputs are labeled \(\mathsf{A}\), \(\mathsf{B}\), \(\mathsf{C}\) and \(\mathsf{D}\), and the resulting output is represented as \(\mathsf{OR}\). This gate yields a high output (\(\mathsf{1}\)) when any of the inputs is high; otherwise, the output remains low (\(\mathsf{0}\)). The table captures every possible combination of inputs along with their corresponding output values. The truth table is presented after the OR gate symbol that corresponds with the truth table.

Can we Implement Multi-Input Gate Using 2-Input Gates in a Cascade?

A gate cascade refers to a structured arrangement where multiple logic gates are connected in series or in levels, so the output of one gate feeds into the input of another. This is especially common when you need to implement complex logic using simpler, typically 2-input gates — like building a 4-input OR using a cascade of 2-input OR gates. This changes the timings and other characteristics of the gate but our goal is to analyze if the logical behavior remains the same?

Implementing a 3-Input OR Gate Using 2-Input OR Gates

This circuit implements a 3-input OR gate using cascaded 2-input OR gates. Due to the associative nature of OR logic, the behavior remains identical to a single 3-input gate, and input ordering does not affect the final output. Readers are encouraged to construct truth tables for the configuration and compare the outputs to those of a canonical 3-input OR gate. This verification highlights that the logical behavior remains consistent, regardless of the gate arrangement or input order.

Implementing a 4-Input OR Gate Using 2-Input OR Gates

This illustration demonstrates a 4-input OR gate constructed using cascaded 2-input OR gates. Two implementations are provided: one with two levels of cascading, and another using three distinct levels of 2-input gates. Because OR operations are associative, both versions produce logically equivalent outputs regardless of input order. Readers are encouraged to generate truth tables based on each configuration and compare them against the canonical 4-input OR gate to confirm identical logical behavior.

Basic Quiz about OR Gates