The given problem asks us to find the minimum value of m * n, where m represents the number of input lines and n represents the number of output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM.

To address a byte addressable 1 KB RAM, we need a total of 1024 memory locations (as 1 KB = 1024 bytes). Each memory location needs to be uniquely addressed using the decoder.

Let's break down the problem into smaller steps to find the minimum value of m * n:

1. Determine the number of address bits required:
- Each memory location needs a unique address, and we have 1024 memory locations.
- To represent 1024 unique addresses, we need log2(1024) = 10 bits. This means we need a 10-bit address.

2. Determine the number of output lines (n):
- The number of output lines (n) represents the number of unique addresses that can be generated by the decoder.
- For a 10-bit address, the number of unique addresses that can be generated is 2^10 = 1024.
- Therefore, n = 1024.

3. Determine the number of input lines (m):
- The number of input lines (m) represents the number of address bits required to generate the unique addresses.
- In this case, m is equal to the number of bits in the address, which is 10.
- Therefore, m = 10.

4. Calculate the minimum value of m * n:
- m * n = 10 * 1024 = 10240.

However, we need to find the minimum value of m * n. Since m = 10 and n = 1024 are the minimum possible values for this scenario, the minimum value of m * n is 10 * 1024 = 10,240.

But the correct answer is given as 1034. It seems like there might be an error either in the question or the provided correct answer. Based on the given information, the minimum value of m * n should be 10,240, not 1034.