hexadecimal format

[apoorba mohapatra]

Question 15
-----------
class JJF5 {
public static void main(String args[]) {
System.out.print(Integer.toHexString(Integer.MIN_VALUE)+",");
System.out.print(Integer.toHexString(Integer.MAX_VALUE));
}}


from [http://www.danchisholm.net/dec20/guide/chapter2/exam1.html]

How should I calculate the output?
Int has min value -2^ 31.
So do we need to convert that value to hexadecimal form and get the output?
But calculating this stuff would be very lengthy.

BTW the answer is: Prints: 80000000,7fffffff

[Chandrakanth]

System.out.print(Integer.toHexString(Integer.MIN_VALUE)+",");
System.out.print(Integer.toHexString(Integer.MAX_VALUE));

Int is 32bits (with 1 sign bit)
so Min value of int(which is -ve) in its hex representation is
for -ve sign bit is 1
for +ve sign bit is 0

Sign Bit + 31 zeros
1 000 0000 0000 0000 0000 0000 0000 0000 [min value of int]
so output is: 80000000

Max Value is +ve
Sign Bit + 31 1's
0 111 1111 1111 1111 1111 1111 1111 1111
so output is: 7fffffff

[Enge Chall]

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 ]

[Bert Bates]

Hi Guys -

Just to clarify, this topic is on the 1.4 exam, but it's NOT on the Tiger exam...

carry on

[Enge Chall]

The algorithm looks tiger because of 32 bits. The same could be imagined for 4 bits for simplicity. cheers

In case someone gets any other -ve number, they can immediately pick the answer.

[ghal prad]

I need that 4 bits procedure for simplicity
I have not understood this.

Can some ome help please?

[Enge Chall]

What exactly you need in the 4 bit ?

Just take off all the 1's and 0's keeping the MSB and right side 3 bits as it is. That cut-shorts the procedure.

does that answer ?