The Logic Gate that provides High Output for same inputs is X-NOR gate.

Explanation:
The X-NOR gate is a digital logic gate that outputs a high (1) signal only when its two binary inputs are the same. In other words, it provides a high output when both inputs are either 0 or 1.

Truth Table:
To understand the behavior of the X-NOR gate, let's look at its truth table:

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

From the truth table, we can observe that the X-NOR gate outputs a high (1) signal only when both inputs are the same. When both inputs are 0 or both inputs are 1, the X-NOR gate provides a high output.

Application:
The X-NOR gate is commonly used in various digital circuits and applications, such as:
1. Comparators: X-NOR gates can be used to compare two binary numbers or signals and determine if they are equal.
2. Parity Checkers: X-NOR gates are used to perform parity checks on data to detect errors.
3. Adders: X-NOR gates are used in the construction of adder circuits for binary arithmetic operations.
4. Multiplexers: X-NOR gates are used in multiplexer circuits to select one of multiple input signals based on control inputs.

Conclusion:
The X-NOR gate is the logic gate that provides a high output for the same inputs. It is a fundamental building block of digital logic circuits and finds applications in various fields of computer science and engineering.