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How to make one BigInteger from a 4 byte number

The essence of the task is this, I encode the bytes of the file, 1 byte of the source file = 4 bytes of the encrypted one. For example, the encoded byte is 3125890409. In byte representation, this is [186, 81, 77, 105]. For decryption, I must present this array as a single number. How can I first convert these 4 numbers to binary, and then to decimal and assign BigIntger? I thought to do it like this:
for(int i = 0; i < fileData2.length; i+=4) {
BigInteger message = BigInteger.valueOf(fileData2[i]);
BigInteger message2 = BigInteger.valueOf(fileData2[i + 1]);
BigInteger message3 = BigInteger.valueOf(fileData2[i + 2]);
BigInteger message4 = BigInteger.valueOf(fileData2[i + 3]);
}
And then translate each into binary, but it looks too complicated, and what if you need to do not 4 bytes, but 8 bytes and higher. How can it be implemented faster?

Do not bother with BigInteger or BigDecimals. Instead think of your original byte as one byte (or 8 bits), and the encoded/encrypted values as 4 bytes (32 bits). If you just shove them into a byte[] you can choose an arbitrary size - be it 4, 8, or 13. Lots of flexibility there.
This approach makes it also easier to read/write the data, as you might simply serialize the bytes into a stream//read the data from a stream, as it feels quite natural to read and write the low indexes of the array first.
Once done with that, all you have to focus on is your function to turn 8 bits into 32 bits and vice versa.

4 bytes fit in an int. Though a negative one here. Use a long otherwise. The byte order seems to be big endian, most significant byte first - it is an odd number as is the last byte.
byte[] fileData = {(byte)186, 81, 77, 105};
int n = new BigInteger(fileData).intValue();
int n = ByteBuffer.wrap(fileData).byteOrder(ByteOrder.BIG_ENDIAN).getInt();
long nn = n & 0xFF_FF_FF_FFL;
BIG_ENDIAN is the default, so the byteOrder is not needed here.

How to convert negative byte value to either short or integer?

We have a file which contains byte array in particular format like header and then followed by data. This file is generated by another java program and then we are reading that same file through another java program in the same format in which it was written.
The program which is making that file, populates lengthOfKey as byte which is right as that's what we need as shown below.
for (Map.Entry<byte[], byte[]> entry : holder.entrySet()) {
byte typeKey = 0;
// getting the key length as byte (that's what we need to do)
byte lengthOfKey = (byte) entry.getKey().length;
byte[] actualKey = entry.getKey();
}
Now as byte can only store maximum value as 127, we are seeing for some of our record lengthOfKey is coming as negative while we read the file as shown below:
Program which is reading the file:
byte keyType = dis.readByte();
// for some record this is coming as negative. For example -74
byte lengthOfKey = dis.readByte();
Now my question is : Is there any way I can find out what was the actual length of key because of that it got converted to -74 while writing it. I mean it should be greater than 127 and that's why it got converted to -74 but what was the actual value?
I think question would be how to convert negative byte value to either short or integer? I just wanted to verify to see what was the actual length of key because of that it got converted to negative value.

If the original length from entry.getKey().length is greater than 255, then the actual length information is lost. However, if the original length was between 128 and 255, then it can be retrieved.
The narrowing conversion of casting to byte keeps only the least significant 8 bits, but the 8th bit is now interpreted as -128 instead of 128.
You can perform a bit-and operation with 0xFF, which will retain all bits, but that implicitly widens the value back to an int.
int length = lengthOfKey & 0xFF;
lengthOfKey (byte = -74): 10110110
Widening it to an int, with sign extension:
lengthOfKey (int = -74): 11111111 11111111 11111111 10110110
Masking out the last 8 bits as an int:
length (int = 182): 00000000 00000000 00000000 10110110
That will convert a negative byte back to a number between 128 and 255.

If you use Guava, it provides a number of unsigned math utilities, including UnsignedBytes.
UnsignedBytes.toInt(lengthOfKey);
Notice their implementation of toInt() is exactly what #rgettman suggests.

To convert an assumed unsigned byte to an int.
int value = (byteValue >= (byte) 0) ? (int) byteValue : 256 + (int) byteValue;

consolidating bytes in java

As part of a program I'm writing I need to consolidate two bytes into a long from an array of bytes.
So assuming this:
byte a[] = new byte[2]
a[0] = 0b1000111
a[1] = 0b1111000
how can I consolidate them such that
long b = 0b10001111111000
EDIT: The program will attempt to consolidate anywhere between 2 bytes and 100, just for reference.

java.nio can do that:
ByteBuffer.wrap(a).getShort()

BigInteger can do this: http://docs.oracle.com/javase/6/docs/api/java/math/BigInteger.html
BigInteger buffer = new BigInteger(yourByteArray);
long result = buffer.longValue();
Note that if your byte array has a value larger than a long (eg, you mentioned that you might go up to 100 bytes), toLong() will only return the value of the lower value bytes. BigInteger, however, will handle any arbitrary number of bytes.

In order to combine those two bytes you will only need 16 bits. A short will suffice:
short result = (short)(((a[0] & 0xff) << 8) | (a[1] & 0xff))
If for some reason, you need the long data type, you need only replace the cast with a long.

Java byte to int

I know there are N threads for this question but some people are using different and different methods to convert a byte to int. Is this correct what am I writing? Hex to int or hex to decimal? Which one is the correct?
Anyway, why I'm getting 4864 instead of 19 ?
byte[] buffer = ....
buffer[51] = 0x13;
System.out.println( buffer[51] << 8 );

Is this correct what am I writing?
The code you've posted does implicit conversion of int to String, but that will display it in decimal. It's important to understand that a number isn't in either hex or decimal - it's just a number. The same number can be converted to different textual representations, and that's when the base matters. Likewise you can express the same number with different literals, so these two statements are exactly equivalent:
int x = 16;
int x = 0x10;
Anyway, why I'm getting 4864 instead of 19
Because you're explicitly shifting the value left 8 bits:
buffer[51] << 8
That's basically multiplying by 256, and 19 * 256 is 4864.

you are getting 4864 as a result because 4864 is 0x1300 in hex.
if you are expecting 19(0x13) as result then I guess you are trying to do circular shifting.
you can do that using writing like that,
/*hex 0x13 (19 in decimal) is assigned to buffer[51] as int*/
buffer[51] = 0x13;
System.out.println( Integer.rotateRight(buffer[51], 8));

Java - converting int to byte array without considering sign

To convert an int into a byte array, I'm using the following code:
int a = 128;
byte[] b = convertIntValueToByteArray(a);
private static byte[] convertIntValueToByteArray(int intValue){
BigInteger bigInteger = BigInteger.valueOf(intValue);
byte[] origByteArray = bigInteger.toByteArray();
byte[] noSignByteArray = new byte[bigInteger.bitLength()/8];
if(bigInteger.bitLength()%8!=0){
noSignByteArray = origByteArray;
}else{
System.arraycopy(origByteArray,1,noSignByteArray,0,noSignByteArray.length);
}
return noSignByteArray;
}
There are two things which I'm attempting to do.
1)I need to know the number of bytes (rounded up to the closes byte) of the original integer. However, I don't need the additional bit that is added for the sign bit when I call the toByteArray() method. This is the reason why I have the helper method. So in this example, if I don't have the helper method, when I convert 128 to a byte array I get the length to be 2 octets because of the sign bit but I'm only expecting it to be one octet.
2)I need the positive representation of the number. In this example, if I attempt to print the first element in array b, I get -128. However, the numbers I will be using will be positive numbers only so what I actually want is 128. I'm limited to using a byte array. Is there a way to accomplish this?
Updated Post
Thank you for the responses. I haven't found the exact answer I was looking for so I'll attempt to give more details. Ultimately, I want to write values of different types over a data output stream. In this post, I'd like to clarify what happens when ints are written to a data output stream. I've come across two scenarios.
1)
DataOutputStream os = new DataOutputStream(this.socket.getOutputStream());
byte[] b = BigInteger.valueOf(128).toByteArray();
os.write(b);
2)
DataOutputStream os = new DataOutputStream(this.socket.getOutputStream());
os.write(128);
In the first scenario, when the bytes are read from a data input stream, it seems that the first element in the byte array is a 0 to represent the msb and the second element in the array contains the number -128. However, since the msb is 0 we would be able to determine that it is intended to be a positive number. In the second scenario, there is no msb and the only element present in the byte array read from the input stream is -128. I was expecting the write() method of the data output stream to convert the int into the byte array in the same manner as the toByteArray() method does on a BigInteger object. However, this doesn't seem to be the case as the msb is not present. So my question is, how in the second scenario are we supposed to know that 128 is supposed to be a positive number and not a negative one if there is no msb.

As you probably already know
In an octet, the pattern 10000000 can be interpreted as either 128 or -128, depending on the, um, outside interpretation
Java's byte type interprets octects as values in -128...127 only.
If you are building an application in which the entire world consists of nonnegative integers only, then you could simply do all of your work under the assumption that the byte value -128 will mean 128 and -127 will mean 129 and ... and -1 will mean 255. This is certainly doable but it takes work.
Dealing with the notion of an "unsigned byte" like this is normally done by expanding the byte into a short or int with the higher order bits all set to zero and then performing arithmetic or displaying your values. You will need to decide whether such an approach is more to your liking than just representing 128 as two octets in your array.

I think the following code might be sufficient.
In java int is a twos-complements binary number:
-1 = 111...111
ones complement = 000...000; + 1 =
1 = 000...001
So that about the sign bit I do not understand. Be it, that you could do Math.abs(n).
A byte ranges from -128 to 127, but the interpretation is a matter of masking, as below.
public static void main(String[] args) {
int n = 128;
byte[] bytes = intToFlexBytes(n);
for (byte b: bytes)
System.out.println("byte " + (((int)b) & 0xFF));
}
public static byte[] intToFlexBytes(int n) {
// Convert int to byte[4], via a ByteBuffer:
byte[] bytes = new byte[4];
ByteBuffer bb = ByteBuffer.allocateDirect(4);
bb.asIntBuffer().put(n);
bb.position(0);
bb.get(bytes);
// Leading bytes with 0:
int i = 0;
while (i < 4 && bytes[i] == 0)
++i;
// Shorten bytes array if needed:
if (i != 0) {
byte[] shortenedBytes = new byte[4 - i];
for (int j = i; j < 4; ++j) {
shortenedBytes[j - i] = bytes[j]; // System.arrayCopy not needed.
}
bytes = shortenedBytes;
}
return bytes;
}

To answer your first question—how many bytes are required to represent a nonnegative integer using an unsigned representation—consider the following functions I wrote in Common Lisp.
(defconstant +bits-per-byte+ 8)
(defun bit-length (n)
(check-type n (integer 0) "a nonnegative integer")
(if (zerop n)
1
(1+ (floor (log n 2)))))
(defun bytes-for-bits (n)
(check-type n (integer 1) "a positive integer")
(values (ceiling n +bits-per-byte+)))
These highlight the mathematical underpinnings of the problem: namely, the logarithm tells you how many powers of two (as provided by bits) it takes to dominate a given nonnegative integer, adjusted to be a step function with floor, and the number of bytes it takes to hold that number of bits again as a step function, this time adjusted with ceiling.
Note that the number zero is intolerable as input to a logarithm function, so we avoid it explicitly. You may observe that the bit-length function could also be written with a slight transformation of the core expression:
(defun bit-length-alt (n)
(check-type n (integer 0) "a nonnegative integer")
(values (ceiling (log (1+ n) 2))))
Unfortunately, as the logarithm of one is always zero, regardless of the base, this version says that the integer zero can be represented by zero bits, which isn't the answer we want.
For your second goal, you can use the functions I've defined above to allocate the required number of bytes, and incrementally set the bits you need, ignoring sign. It's hard to tell if you're having trouble getting the proper bits set in the byte vector, or whether your problem is in interpreting the bits in way that avoids treating the high bit as a sign bit (that is, two's complement representation). Please elaborate what kind of push you need to get you moving again.