Binary Representation of Integer.MIN_VALUE

Question

The binary representation of Integer.MIN_VALUE in Java is 10000000000000000000000000000000 .

Why wouldn't it be 10000000000000000000000000000001 instead, since the addition of one to its two's complement would be larger than 10000000000000000000000000000000 by one?

Answer 1

int in Java is a signed 32-bit number, meaning that the 32th bit, like you said, represents the negative number, in decimal, -(2^31) , and in binary:

10000000000000000000000000000000
^ → "negative bit"

But the remaining 31 bits are still "positive" bits in a signed system, so:

10000000000000000000000000000001 → -2^31 + 1

And -2^31 + 1 is bigger than -2^31 .