NAND and NOR gates are called universal gates primarily because they
A) are available universally
B) can be combined to produce OR, AND, and NOT gates
C)are widely used in the integrated circuit package
D)are easiest to manufacture
Hint: Logic gates perform mathematical operations within integrated circuits (ICs). There are seven primary types of gates: AND, OR, NOT, NAND, NOR, XOR, and XNOR. Among these, NAND and NOR gates are classified as universal gates.
Step-by-Step Explanation:
NAND and NOR gates can replicate the functions of all other gate types, including logical AND, OR, and NOT operations.
The following points outline the input-output relationships for NAND and NOR gates:
NOR Gates: A NOR gate can be transformed into a NOT gate by connecting its inputs together. This conversion highlights that a NOR gate operates as an OR gate followed by a NOT operation, effectively disregarding the OR aspect.
OR Gates from NOR: To convert a NOR gate into an OR gate, you can attach a NOT gate to its output. This results in the output of the combined gates being the inverse of the OR gate output for the same inputs.
AND Gates from NOR: An AND gate produces an output of 1 only when both of its inputs are 1. To create an AND gate, you can invert the inputs of a NOR gate.
NOT Gates from NAND: A NAND gate can serve as a NOT gate by tying its inputs together.
Complex Gates: Beyond AND, OR, and NOT operations, NAND gates can also be combined to create XOR and NOR operations.
An example of constructing an XOR gate using NAND gates is illustrated below:
IC Requirements: Each type of logic gate requires specific ICs. For instance, an AND gate is implemented using IC 7408. However, with the IC 7400 (for NAND gates), one can build any logic gate using just that single type. The same applies to NOR gates as well.
In conclusion, NAND and NOR gates are termed universal gates because they can be used to construct any of the other gates, such as AND, OR, and NOT. Thus, the correct answer is option (B).
Note: While AND and NOR gates can meet various requirements in the question, the reason for calling NAND and NOR universal gates highlights that option (B) is the sole choice. Both NAND and NOR gates are cost-effective and widely utilized in many integrated circuit designs.
