Read and convert binary files to ASCII text
Aside from turning StringBuffer into StringBuilder, there are a few more things I'd like to note about your code.

Compound assignment operator

This line:

 lastString = lastString + line;


Can be rewritten as this one:

 lastString += line;


It's short and it complies with what many people would expect: a concatenation. By explicitly mentioning the original variable again, many people might think it is a different variable before looking at it more closely.

Additionally, you might also want to add a StringBuilder to the reading of the file. Even if the inputfile isn't that big, it would still be consistent.

Magic values

Consider this code:

for (int i = 0; i &lt; lastString.length(); i += 8) {
     result.append((char) Integer.parseInt(lastString.substring(i, i + 8), 2));
}


Can someone other than the authro tell with certainty what the value 8 is? An educated guess would lead to the bit representation of 2 bytes, but we shouldn't have to guess that. Get rid of this so called "magic value" by adding a variable which clears it up:

int amountOfBits = 8;
for (int i = 0; i &lt; lastString.length(); i += amountOfBits ) {
     result.append((char) Integer.parseInt(lastString.substring(i, i + amountOfBits ), 2));
}


Exception handling

You're completely bypassing exception handling. I'm assuming this is just so this contrived sample wouldn't get cluttered with code, but just in case it isn't:

throws Exception


is always a bad idea in an actual program. You should catch the exact exception and handle it appropriately.