Don't confuse

**two's complement** binary notation which purely mathematical

**base two** binary notation. In two's complement, we have something called a sign bit, which is meaningless in pure mathematics. That base-two digit all the way on the left of your number is not a sign bit in base two; it's only a sign bit in two's complement. When you call parseInt and tell it to use a radix of 2, you're saying that

**the String should be evaluated as a base two number, NOT as a two's complement bit pattern**.

So if the leftmost digit is not a sign bit in base two, what is it? It's just another digit. It's the digit that represents the 2147483648 column. So if a 1 is in that column, and there is no negative sign on this ordinary base-two number, the number must be 2147483648 or more, which is a value that will not fit into an int. I suspect that the NumberFormatException is caused by the fact that the String you entered, when translated to base two (not two's complement) is not a valid int value. It's too high.

Here's a short program to see the powers of 2 from 0 to 31.

You entered the number

**1**1111111111111111111111111111101

The rightmost column is the 1 column. The next column is the 2 column, then the 4 column, and so on all the way to the left side, where we reach the 2147483648 column. There's a 1 in that column, and the number is positive because there is no negative sign (remember, there's no "sign bit" in a regular base two number). Therefore, the number is greater than 2147483648, so it's too big for an int.

[ May 11, 2005: Message edited by: Joe Sanowitz ]