If there are $m$ input lines and $n$ output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of $m + n$ is ________.

For a byte-addressable $1\text{ KB}$ RAM:

1. Total memory capacity $= 1\text{ KB} = 1024\text{ bytes}$.

2. Since each byte requires a unique address, there are $1024$ distinct locations to address.

3. A decoder used to uniquely select one of the $1024$ locations must have:

   • Number of output lines, $n = 1024$.

   • Number of input (address) lines, $m = \log_2(1024) = 10$.

Therefore, the minimum value of $m + n$ is: