In the given problem, we have 2020 true coins, each weighing an even number of grams, and 2 false coins, each weighing an odd number of grams. The electronic device available can detect the parity (even or odd) of the total weight of a set of coins. We need to determine the minimum number of measurements, $k$, required to identify the two false coins using this parity information.

The key insight is that each measurement provides a single bit of information (even or odd), and we use these bits to gradually identify the false coins among the total 2022 coins (2020 true + 2 false).

### Strategy to Identify the False Coins:

1. Understanding Parity Checks:
- The even number of grams for the true coins will give an even total parity when weighed in any even numbers.
- Any odd number of grams, when added to the even total, will result in an odd parity.

2. Binary Cutting Technique:
- Similar to a binary search, we can narrow down the possible false coins by half with each parity check.
- The primary goal is to ensure that the number of possible combinations after each measurement is reduced significantly, ideally halved.

3. Calculation of Minimum Measurements:
- With $n = 2022$ coins, our task is to identify 2 specific false coins.
- Given that each measurement provides one bit of information, and knowing the initial uncertainty involves differentiating the 2 out of 2022, this is equivalent to differentiating among $\binom{2022}{2} \approx 2,041,231$ possible pairs of coins.
- Thus, the number of measurements required to determine these false coins is given by the smallest $k$ such that:
$$2^k \geq \binom{2022}{2}$$

4. **Calculate the Smallest $k$:**
- We approximate:
- $\log_2(\binom{2022}{2}) \approx \log_2(2,041,231) \approx 21.0$.
- Hence, the smallest integer $k$ satisfying this inequality is $k = 21$.

Therefore, the minimum number of measurements required to definitively identify the two false coins using the electronic device is:
$$\boxed{21}$$