Converting 32-bit binary string with Integer.parseInt fails

Question

Why does this part of code fail:

Integer.parseInt("11000000000000000000000000000000",2);

Exception in thread "main" java.lang.NumberFormatException: For input string: "11000000000000000000000000000000"

As far as I understand Integer is a 32 bit value. The number of zeros and ones in the upper code is 32. If there are 31 the code works. Why is that so?

Solution 1

Your code fails because it tries to parse a number that would require 33 bits to store as a signed integer.

A signed int is a 32 bit value in two's complement representation, where the first bit will indicate the sign of the number, and the remaining 31 bits the value of the number. (-ish.) Java only supports signed integers, and parseInt() and friends aren't supposed to parse two's complement bit patterns – and thus interpret the 1 or (possibly implied) 0 at the 32nd position from the right as the sign. They're meant to support parsing a human-readable reprentation, which is an optional - (or +) for the sign, followed by the absolute value of a number.

In this context, it's a false intuition that leads you to expect the behaviour you describe: if you were parsing any other base besides base 2 (or maybe the other commonly used power-of-two bases), would you expect the first digit of the input to affect the sign? Obviously you wouldn't; having, say, parseInt("2147483648") return -2147483648 by design would be PHP levels of crazy.

Special-casing power-of-two bases also feels odd. Better to have a separate approach to handling bit patterns, for example the one in this answer.

Solution 2

According to the docs, the max value of an Integer is 2^31-1. Which, in binary is:

1111111111111111111111111111111

In other words, 31 1's in a row.

Solution 3

This is because for Integer.parseInt "11000000000000000000000000000000" is not a two's complement representation of -1073741824 but a positive value 3221225472 which does not fit into int values range -2147483648 to 2147483647. But we can parse two's complement binary string representation with BigInteger:

int i = new BigInteger("11000000000000000000000000000000", 2).intValue()

this gives expected -1073741824 result

Comments

[user949300]

I just reread the javadocs for Integer.parseInt() yet again, and I do not see anything saying "this doesn't parse negative numbers" (in fact, it says "signed int"), or, at least explicitly, "this doesn't parse bit patterns". In fact, as described in the javadocs, one could argue that a String of 55 0s should parse to 0. I consider the behavior a bug. But doesn't look like Oracle or OpenJDK will fix it. Do you see anything in the javadocs to contradict this?

[Montre]

@user949300 parseInt will parse negative binary numbers, if you pass them in as, say, "-10010110". It will also parse a string of 55 zeroes, because it's a valid value for an int. A 32-bit number without leading zeroes is not a valid int value, and so it's rejected.

[Montre]

@user949300 What I meant by "won't parse bit patterns" is that what `Integer.parseInt(str, 2)" parses is a number written in base 2. It does not parse a stringified two's complement binary representation of a 32-bit integer. I don't consider this a bug, I just consider it something the method is not intended for – which is parsing "human" textual representations of numbers in arbitrary bases.

[user949300]

@Interdial Hmm, I didn't think 55 zeros worked. Thanks for testing! I think it's strange that 55 0s works and 32 1s don't, but that's the way it is.

[Oliver Charlesworth]

Java represents integers in 2's-complement, not sign-magnitude.

[jlordo]

To support what Oli Charlesworth just said, have a look at this question: Java, Long.parse binary String

[jlordo]

It's not a bug. JavaDoc states, that if you want a negative Integer from parseInt(), you have to have an ASCII minus - at the beginning of the String. Have look at this question: Java, Long.parse binary String

[Montre]

@OliCharlesworth Right, I rephrased the answer.

[Montre]

@jlordo Supporting his comment by another comment of his saying this very answer is wrong, just elsewhere? I thought that only works in liberal arts and punditry ;)

[jlordo]

@millimoose: Yesterday's question brought us here, and after I saw Oli comment, I thought it would be fair to link to the new question. Wasn't meant as an offence, and my -1 is now a +1 ;)