Question

How many NAND gates are used to form AND gate? (A) 1 (B) 2 (C) 3 (D) 4

Short answer

Three NAND gates are used to form an AND gate.

Step-by-step solution

Recall the Truth Table for AND and NAND Gates

First, let's recall the truth table for AND and NAND gates: AND Gate: Input A | Input B | Output (A AND B) 0 | 0 | 0 0 | 1 | 0 1 | 0 | 0 1 | 1 | 1 NAND Gate: Input A | Input B | Output (A NAND B) 0 | 0 | 1 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The objective is to use multiple NAND gates in such a way that the overall output is equivalent to an AND gate.

Creating the AND gate using NAND gates

Suppose we have three NAND gates. Let's label them NAND1, NAND2, and NAND3. We will connect these gates in the following manner: - Connect the inputs A and B to the inputs of NAND1. - Connect the output of NAND1 to both inputs of NAND2. - Connect the output of NAND2 to both inputs of NAND3. Now, let's analyze the output of each NAND gate based on the inputs A and B: 1. If A = 0, B = 0: - Output of NAND1 = 1; since NAND1 input is (0,0) - Output of NAND2 = 0; since NAND2 input is (1,1) - Output of NAND3 = 1; since NAND3 input is (0,0) - Overall Output = 0; which is equivalent to AND gate output for input (0,0) 2. If A = 0, B = 1: - Output of NAND1 = 1; since NAND1 input is (0,1) - Output of NAND2 = 0; since NAND2 input is (1,1) - Output of NAND3 = 1; since NAND3 input is (0,0) - Overall Output = 0; which is equivalent to AND gate output for input (0,1) 3. If A = 1, B = 0: - Output of NAND1 = 1; since NAND1 input is (1,0) - Output of NAND2 = 0; since NAND2 input is (1,1) - Output of NAND3 = 1; since NAND3 input is (0,0) - Overall Output = 0; which is equivalent to AND gate output for input (1,0) 4. If A = 1, B = 1: - Output of NAND1 = 0; since NAND1 input is (1,1) - Output of NAND2 = 1; since NAND2 input is (0,0) - Output of NAND3 = 1; since NAND3 input is (1,1) - Overall Output = 1; which is equivalent to AND gate output for input (1,1) As you can see, by connecting three NAND gates in the manner mentioned above, we have created an AND gate. Therefore, the correct answer is: (C) 3

Key concepts

NAND Gate

A NAND gate is essential in digital electronics. It is a universal gate, which means you can use it to create any other type of logic gate, including AND, OR, and NOT gates. The NAND gate will give an output of 0 only when both inputs are 1. In all other cases, the output will be 1. This behavior is unique and allows for its versatility in circuits.
The truth table for a NAND gate, as highlighted, looks like this:

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

This ability to easily toggle output based on inputs makes it a favorite among engineers when designing complex circuits.

AND Gate

An AND gate is one of the most straightforward logic gates. It performs a simple logical operation that outputs true or 1 only when both of its binary inputs are true or 1. Otherwise, the output is false or 0. This characteristic makes it very intuitive and easy to understand.
The truth table for an AND gate is straightforward:

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

Understanding how AND gates work is fundamental, as they are building blocks of numerous more complex digital systems. They are often used where a condition needs to satisfy multiple criteria before proceeding.

Truth Table

A truth table is a valuable tool in digital electronics. It shows all possible input combinations and their respective outputs for a logic gate or circuit. By looking at a truth table, you can predict how a logic circuit will behave in any situation.
For instance, the truth tables for AND and NAND gates clearly demonstrate how each combination of inputs results in a specific output. It helps in visualizing and understanding complex logical operations in simpler terms.
Using truth tables is crucial when designing, testing, or explaining logic circuits, as they provide a systematic way of exploring each scenario. They also serve as a reference guide for creating more advanced logic configurations.

Logic Gates

Logic gates are the fundamental building blocks of digital circuits. They perform basic logical functions that are the essence of digital electronics. Every complex circuit is essentially a combination of these gates working in unison to perform specific tasks or operations. The primary types of logic gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each has a unique functionality that allows it to execute fundamental logical operations.
By combining different logic gates, engineers and designers can create circuits to perform various tasks, from simple operations like addition to controlling complex systems in computers or automated machines.
Understanding how these gates function is crucial for anyone interested in electronics or computer science, offering the knowledge needed to create intricate and reliable electronic systems.