Which type of logic gate is commonly used in the design of a magnitude comparator?a.NAND gateb.AND gatec.OR gated.XOR gate

To determine which type of logic gate is commonly used in the design of a magnitude comparator, let's analyze the options provided.

1. Understanding the Function of a Magnitude Comparator: A magnitude comparator is a digital circuit that compares two binary numbers and outputs the result indicating whether one is greater than, less than, or equal to the other.

2. Role of Logic Gates:

   • NAND Gate: This gate is a universal gate and can be used to create any other type of gate or function, but it is not specifically used for comparison operations.
   • AND Gate: This gate outputs true only if all its inputs are true, which does not suffice for comparing magnitudes.
   • OR Gate: Similar to the AND gate, it combines inputs but does not effectively serve to compare binary numbers directly.
   • XOR Gate: The XOR (exclusive OR) gate outputs true only when the number of true inputs is odd. This property is essential for comparing bits between two binary numbers—indicating where they differ.

3. Conclusion: In the context of magnitude comparators, the XOR gate is particularly effective for determining inequality between inputs, making it the most commonly used type of gate in their design.

Final Answer

d. XOR gate