Your binaryString was declared as an array of constantchars.
Also, the array currently has a size of 0, and there is no need to have your variables global. Keep them inside main() otherwise the variable name on line 27 shadows your global variable and variable used on line 30 is ambiguous.
Constant variables cannot be modified. Simply remove the const qualifier, so you can change the values in your array. Also make sure your array has sufficient space to store the values.
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char user_input[80] = "\0";
std::cin.getline(user_input, 80); //This is for reading character arrays