Hi Apoorba, further to make it simple to face simillar questions you must be familliar with one's complement and two's complement in your studies.
It goes like this:
'-' ve numbers are represented in 2's complement form in computer memory.
What is 2's complement form ? Ans: It's one's complement + 1 ie add 1 to one's complement.
What is one's complement ? Ans: Just alter the digits of your binary numbers. ( if 1 make it 0, if 0 make it 1 ).
How -1 is represented ? Ans: It's 1 with a -ve sign ie two's complement of +1 with a -ve sign.
What is -ve sign and +ve sign ? Ans: The MSB is switched on ( ie MSB is 1 for -ve ), MSB is switched off( ie MSB is 0 for +ve ).
What is MSB ? Ans: The left most bit called Most Significant Bit .
==> let's eg: find out how -1 is stored in computer <==
So keeping that in mind now find out the 2's complement of 1. As
java int is 4 bytes ie 32 bits, the 32nd bit is the MSB.
Now let's calculate:
+1 is 0000 0000 0000 0000 0000 0000 0000 0001
-1 is 2's complement of +1 ie 1's complement of +1 added by 1 as below :
1111 1111 1111 1111 1111 1111 1111 1110 +
0000 0000 0000 0000 0000 0000 0000 0001
---------------------------------------
1111 1111 1111 1111 1111 1111 1111 1111 ( See here MSB is switched on automatically for -ve )
Now coming to your question ie -2^31 is the minimum -ve value of int in java ( I am sure , you know how ? )
Now let's calculate:
+2^31 is 1000 0000 0000 0000 0000 0000 0000 0000
-2^31 is 2's complement of +2^31 ie 1's complement of +2^31 added by 1 as below :
0111 1111 1111 1111 1111 1111 1111 1111 +
0000 0000 0000 0000 0000 0000 0000 0001
---------------------------------------
1000 0000 0000 0000 0000 0000 0000 0000 ( See here MSB is switched on automatically for -ve )
Now convert to hexa : 80000000 ( every 4 bits together )
Simillarly with +ve numbers MSB is 0 ( switched off ).
Max +ve number is => (2^32)-1 ie
0111 1111 1111 1111 1111 1111 1111 1111 ( No calculation requires here as it is stored as it is )
So hex of this is : 7FFFFFFF
PLEASE LET ME KNOW IF YOU NEED SHORTCUT TO THIS PROCEDURE TO CALCULATE FASTER.
Wish you GOOD LUCK for your
SCJP...

[ December 07, 2005: Message edited by: Enge Chall ]