You need to specify the radix. There's an overload of Integer#parseInt() which allows you to.

int foo = Integer.parseInt("1001", 2);

atoi doesn't handle binary numbers, it just interprets them as big decimal numbers. Your problem is that it's too high and you get an integer overflow due to it being interpreted as decimal number.

The solution would be to use stoi, stol or stoll that got added to string in C++11. Call them like

int i = std::stoi("01000101", nullptr, 2);

• The returned value is the converted int value.
• The first argument is the std::string you want to convert.
• The second is a size_t * where it'll save the index of the first non digit character.
• The third is an int that corresponds to the base that'll be used for conversion..

For information on the functions look at its cppreference page.

Note that there are also pre C++11 functions with nearly the same name, as example: strtol compared to the C++11 stol.
They do work for different bases too, but they don't do the error handling in the same way (they especially lack when no conversion could be done on the given string at all e.g trying to convert "hello" to a string) and you should probably prefer the C++11 versions.

To make my point, passing "Hello" to both strtol and the C++11 stol would lead to:

• strtol returns 0 and doesn't give you any way to identify it as error,
• stol from C++11 throws std::invalid_argument and indicates that something is wrong.

Falsely interpreting something like "Hello" as integers might lead to bugs and should be avoided in my opinion.

But for completeness sake a link to its cppreference page too.

As explained above, Integer.toBinaryString() converts ~0 and ~1 to unsigned int so they will exceed Integer.MAX_VALUE.

You could use long to parse and convert back to int as below.

int base = 2;
for (Integer num : new Integer[] {~0, ~1}) {
    String binaryString = Integer.toBinaryString(num);            
    Long decimal = Long.parseLong(binaryString, base);
    System.out.println("INPUT=" + binaryString + " decimal=" + decimal.intValue()) ;
}

You use the built-in int() function, and pass it the base of the input number, i.e. 2 for a binary number:

>>> int('11111111', 2)
255

Here is documentation for Python 2, and for Python 3.