The truth table for the SUM output of a half-adder is equivalent to a(n):Question 2Answera.NOT gateb.NOR gatec.XOR gated.AND gate

Step 1: Break Down the Problem

To determine what type of gate the SUM output of a half-adder corresponds to, we need to analyze the behavior of the half-adder's SUM output. A half-adder takes two binary inputs (let's call them A and B) and produces two outputs: the SUM and the CARRY.

Step 2: Relevant Concepts

The key logic gates to consider are:

• XOR Gate: Outputs true if the number of true inputs is odd.
• AND Gate: Outputs true only if all inputs are true.
• OR Gate: Outputs true if at least one input is true.
• NOT Gate: Outputs the inverse of the input.
• NOR Gate: Outputs true only if both inputs are false.

Step 3: Analysis and Detail

The SUM output of a half-adder can be defined as: $\text{SUM} = A \oplus B$ Where $\oplus$ denotes the XOR operation. The truth table for SUM is as follows:

From the truth table, we can see that the output (SUM) is 1 when exactly one of the inputs is true, which aligns with the behavior of an XOR gate.

Step 4: Verify and Summarize

Given the truth table analysis, it is clear that the SUM output of a half-adder corresponds to the behavior of an XOR gate.

Final Answer

c. XOR gate