The XNOR gate is a logical gate that produces a HIGH output when two inputs are equal and a LOW output when the inputs are different. Let's apply the inputs A=100101 and B=110110 to the XNOR gate and determine the output.

1. Understanding the XNOR gate:
The XNOR gate is an electronic circuit with two inputs and one output. It follows the truth table:

| Input A | Input B | Output |
|---------|---------|--------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

2. Converting inputs A and B to decimal:
To analyze the output, we need to convert the binary inputs A and B to decimal.

A = 100101 in binary = 37 in decimal
B = 110110 in binary = 54 in decimal

3. Applying the inputs to the XNOR gate:
Now, let's evaluate the inputs A=37 and B=54 in the XNOR gate.

A = 37, B = 54
A in binary = 100101
B in binary = 110110

4. Comparing the binary inputs:
To determine the output, we need to compare the binary representations of A and B bit by bit.

100101
110110

5. Evaluating the comparison:
Starting from the leftmost bit, we compare each corresponding bit of A and B.

1 is not equal to 1 -> Different
0 is not equal to 1 -> Different
0 is equal to 0 -> Same
1 is not equal to 1 -> Different
0 is equal to 0 -> Same
1 is not equal to 0 -> Different

6. Determining the output:
Since the inputs A and B are different in three out of six bits, the output of the XNOR gate will be LOW, which corresponds to a logical value of 0.

Therefore, the output of the XNOR gate for inputs A=100101 and B=110110 is 0.

In summary, when applying the inputs A=100101 and B=110110 to the XNOR gate, the output will be 0. The XNOR gate compares the binary representation of the inputs bit by bit and produces a LOW output when the inputs are different.