Question

To obtain OR gate from NOR gate, you will need (A) one NOR gate (B) one NOT gate (C) Two NOR gate (D) one OR gate

Short answer

The correct choice to obtain an OR gate from NOR gates is (C) Two NOR gates.

Step-by-step solution

Understand OR and NOR Gates

The OR gate is a digital logic gate that implements logical disjunction. It gives an output of 1 (true) if at least one of its inputs is 1 (true). Its symbol and truth table are as follows: OR gate: Input A | Input B | Output --------|---------|------- 0 | 0 | 0 0 | 1 | 1 1 | 0 | 1 1 | 1 | 1 The NOR gate is a digital logic gate that implements the "NOT OR" function, which means its output will be the inverted output of OR gate. Its symbol and truth table are: NOR gate: Input A | Input B | Output --------|---------|------- 0 | 0 | 1 0 | 1 | 0 1 | 0 | 0 1 | 1 | 0

Obtain OR gate from NOR gates

To obtain an OR gate using NOR gates, we will require two NOR gates. The output of the first NOR gate will be inverted, and as a result, we'll obtain the desired OR gate output. The configuration will look like this: Input A --NOR1--> --NOR2--> Output Input B ---------/ The truth table for this configuration would be: Input A | Input B | NOR1 Out | OR Out (NOR2) --------|---------|----------|------------- 0 | 0 | 1 | 0 0 | 1 | 0 | 1 1 | 0 | 0 | 1 1 | 1 | 0 | 1 As we can see, the output of the combined NOR gates matches the truth table of an OR gate.

Analyze the given options

Now, let's analyze each option: (A) one NOR gate: Although NOR gate is closely related to OR gate, it cannot be used directly to obtain the OR gate functionality. (B) one NOT gate: A NOT gate alone cannot provide the function of an OR gate as it just inverts the input. (C) Two NOR gate: As shown in the configuration above, using two NOR gates correctly connected, we can achieve the behavior of an OR gate. (D) one OR gate: Obtaining an OR gate from an OR gate is trivial and not a valid option in this context. After analyzing each option, the correct answer becomes apparent:

Correct Choice

The correct choice to obtain an OR gate from NOR gates is (C) Two NOR gates.

Key concepts

OR Gate

An OR gate is one of the fundamental logic gates used in digital circuits. It represents the logical operation known as disjunction. This means that it outputs a true signal (typically represented by a '1') whenever at least one of its inputs is true. In essence, the operation of the OR gate follows an inclusive rule—the more inputs you have that are "on" or "true," the more certain the output will also be "on" or "true."

Here is how the OR gate functions:

• If both inputs are '0', the output is '0'.
• If one input is '1' and the other is '0', the output is '1'.
• If both inputs are '1', the output is '1'.

The symbol for the OR gate is a curved shape with two input lines and one output line, which helps in recognizing it in circuit diagrams. Its simplistic yet powerful function underscores its widespread use in various applications, ranging from simple alarm circuits to complex computing systems.

NOR Gate

The NOR gate is essentially a combination of two simple operations: NOT and OR. It first calculates an OR operation, then applies a negation to the result. This gate outputs true (or '1') only when all of its inputs are false. Otherwise, it outputs false (or '0'). As such, the NOR gate is recognized as a universal gate because you can implement any logic function using just NOR gates.

Examining the NOR gate's operation:

• If both inputs are '0', the output is '1'.
• If one input is '1' and the other is '0', the output is '0'.
• If both inputs are '1', the output is '0'.

This gate provides a foundational building block in digital electronics, particularly in scenarios where minimal gate types are desired. Using it as the inverse of an OR gate demonstrates its versatility, allowing designers to create OR gate operations using a combination of NOR gates.

Logic Gate Configuration

Logic gate configuration refers to arranging individual logic gates such as OR, AND, and NOR in a circuit to achieve a specific logical operation. Understanding gate configurations is crucial as it paves the way for designing complex digital systems from simple components.

In the exercise, the goal is to achieve the function of an OR gate using two NOR gates:

• The first NOR gate takes two inputs and outputs their NOR result.
• The second NOR gate is used to invert this result, effectively replicating the behavior of an OR gate.

Here is a brief walkthrough of how the configuration works: 1. **Connect inputs A and B to the first NOR gate**: This NOR gate will output true if both A and B are false.
2. **Connect the output of the first NOR gate to both inputs of the second NOR gate**: The second NOR gate inverts the previous output, producing a signal corresponding to the OR truth table.

Such configurations demonstrate the principle of gate equivalency, where one type of logic gate can mimic another through strategic combinations. This is essential in digital computation, providing designers flexibility in circuit design and optimization.