how to convert a hex or binary number to decimal and vice versa using a any java mehtod, can any one help.
and one more thing that can any one explain how computer store and retrieve - sign . i am so much confusd with left and right shifts

i have mentioned 2 codes here.
1). our input variable "int num = 0xFFFFFFE". how after all operations the result
comes in decimal
.
2). we have a String array of hex numbers. how the resultant values are searched in the array.and why weare doing
"[(b >> 4) & 0x0f]" and [b & 0x0f].

any solid reasons

examle1

// Left shifting as a quick way to multiply by 2.
class MultByTwo {
public static void main(String args[]) {
int i;
int num = 0xFFFFFFE;
for(i=0; i<4; i++) {
num = num << 1;
System.out.println(num);
}
}
}

The program generates the following output:
536870908
1073741816
2147483632
-3

example 3

// Masking sign extension.
class HexByte {
static public void main(String args[]) {
char hex[] = {
'0', '1', '2', '3', '4', '5', '6', '7',
'8', '9', 'a', 'b', 'c', 'd', 'e', 'f'
};
byte b = (byte) 0xf1;
System.out.println("b = 0x" + hex[(b >> 4) & 0x0f] + hex[b & 0x0f]);
}
}
Here is the output of this program:
b = 0xf1

Please use the CODE button and maintain indentation; what you quoted is difficult to read.

Your question is too big for a complete answer. I suggest you convert binary to decimal by working from right to left:

Find a decent book, eg Alan Clements the Principles of Computer Hardware Oxford: Oxford University Press (I have 3rd edition (2000) ISBN 0-19-856453-8 but there is a 4th edition at least available). You then find how to convert from decimal to binary in chapter 4, pages 151-158.
You halve the number repeatedly, adding the remainder from right to left to your binary number.

Take a number 9865129

Divide by two, and look for a remainder 4932564 rem 1. The last number of your binary number is 1

Divide by two, and look for a remainder 2466282 rem 0. Add a 0 to the start of your binary number 01

Divide by two, and look for a remainder 1233141 rem 0. Add a 0 to the start of your binary number 001

Divide by two, and look for a remainder 616570 rem 1. Add a 1 to the start of your binary number 1001

Divide by two, and look for a remainder 308285 rem 0. Add a 0 to the start of your binary number 01001

Divide by two, and look for a remainder 154142 rem 1. Add a 1 to the start of your binary number 101001

Divide by two, and look for a remainder 77071 rem 0. Add a 0 to the start of your binary number 0101001

Divide by two, and look for a remainder 38535 rem 1. Add a 1 to the start of your binary number 10101001

Divide by two, and look for a remainder 19267 rem 1. Add a 1 to the start of your binary number 110101001

Divide by two, and look for a remainder 9633 rem 1. Add a 1 to the start of your binary number 1110101001

Divide by two, and look for a remainder 4816 rem 1. Add a 1 to the start of your binary number 11110101001

Divide by two, and look for a remainder 2408 rem 0. Add a 0 to the start of your binary number 011110101001

Divide by two, and look for a remainder 1204 rem 0. Add a 0 to the start of your binary number 0011110101001

Divide by two, and look for a remainder 602 rem 0. Add a 0 to the start of your binary number 00011110101001

Divide by two, and look for a remainder 301 rem 0. Add a 0 to the start of your binary number 000011110101001

Divide by two, and look for a remainder 150 rem 1. Add a 1 to the start of your binary number 1000011110101001

Divide by two, and look for a remainder 75 rem 0. Add a 0 to the start of your binary number 01000011110101001

Divide by two, and look for a remainder 37 rem 1. Add a 1 to the start of your binary number 101000011110101001

Divide by two, and look for a remainder 18 rem 1. Add a 1 to the start of your binary number 1101000011110101001

Divide by two, and look for a remainder 9 rem 0. Add a 0 to the start of your binary number 01101000011110101001

Divide by two, and look for a remainder 4 rem 1. Add a 1 to the start of your binary number 101101000011110101001

Divide by two, and look for a remainder 2 rem 0. Add a 0 to the start of your binary number 0101101000011110101001

Divide by two, and look for a remainder 1 rem 0. Add a 0 to the start of your binary number 00101101000011110101001

Divide by two, and look for a remainder 0 rem 1. Add a 1 to the start of your binary number 100101101000011110101001

Finished.

To convert back repeatedly take the last number off the binary number, and multiply it by a doubling factor.

Start with 0.

Take 100101101000011110101001; last digit is 1, add 1 = 1

Take 10010110100001111010100; last digit is 0, add 2 * 0; total = 1

Take 1001011010000111101010; last digit is 0, add 4 * 0; total = 1

Take 100101101000011110101; last digit is 1, add 8 * 1; total = 9

Take 10010110100001111010; last digit is 0, add 16 * 0; total = 9

Take 1001011010000111101; last digit is 1, add 32 * 1; total = 41

Take 100101101000011110; last digit is 0, add 64 * 0; total = 41

Take 10010110100001111; last digit is 1, add 128 * 1; total = 169

Take 1001011010000111; last digit is 1, add 256 * 1; total = 425

Take 100101101000011; last digit is 1, add 512 * 1; total = 937

Take 10010110100001; last digit is 1, add 1024 * 1; total = 1961

Take 1001011010000; last digit is 0, add 2048 * 0; total = 1961

Take 100101101000; last digit is 0, add 4096 * 0; total = 1961

Take 10010110100; last digit is 0, add 8192 * 0; total = 1961

Take 1001011010; last digit is 0, add 16384 * 0; total = 1961

Take 100101101; last digit is 1 add 32768 * 1; total = 34729

Take 10010110; last digit is 0 add 65536 * 0; total = 34729

Take 1001011; last digit is 1 add 131072 * 1; total = 165801

Take 100101; last digit is 1 add 262144 * 1; total = 427945

Take 10010; last digit is 0 add 524288 * 0; total = 427945

Take 1001; last digit is 1 add 1048576 * 1; total = 1476521

Take 100; last digit is 0 add 2097152 * 0; total = 1476521

Take 10; last digit is 0 add 4194304 * 0; total = 1476521

Take 1; last digit is 1 add 8388608 * 1; total = 9865129