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How to extract and display each of the four bytes of an integer individually as 8-bit values

edit: This question is not a duplicate. The whole point is to solve the question using masks and bit shifts.
I have a terrible programming teacher that introduces concepts without explaining them or providing material to understand them, and he's to arrogant and confrontational too seek help from.
So naturally, I'm stuck on yet another question without any guidance.
Given an integer variable x, write Java code to extract and display each of the four bytes of that integer individually as 8-bit values.
I'm supposed to use masking and bit shift operations to answer this question. I understand that masking means turning bits "on or off" and I understand that an integer has 32 bits or 4 bytes. But that information doesn't help me answer the question. I'm not necessarily asking for the entire solution, but any help would be appreciated.

Using masks and shifting to extract bytes from an integer variable i,
The bytes from most significant (highest) to least are:
byte b3 = (byte)((i>>24));
byte b2 = (byte)((i>>16)&255);
byte b1 = (byte)((i>>8)&255);
byte b0 = (byte)((i)&255);
out.println("The bytes are " + b3 + ", " + b2 + ", " + b1 + ", " + b0);

You could use a ByteBuffer
int myInt = 123;
byte[] bytes = ByteBuffer.allocate(4).putInt(myInt).array();
Then you can do whatever you want with it. If you want all bits you could do something like this:
for(int i = 0; i < 4; i++)
{
for(int j = 0; j < 8; j++)
{
if(bytes[i] & (1 << j))
{
System.out.print("1");
}
else
{
System.out.print("0");
}
}
System.out.print(" ");
}
I have not tested this code because I do not have Java on this PC, but if it does not work let me know. However this sould give you a ruff idea of what has to be done.

Firstly you have to understand bitwise operators and operations. ( https://docs.oracle.com/javase/tutorial/java/nutsandbolts/op3.html )
Boolean logic states that x & 1 = x and x & 0 = 0.
Knowing this we can create a mask for, lets say the least significant 4 bits of an 8 bit number: 11001101 & 00001111 = 1101 (205 & 0x0f = 13).
(we ignore the first 4 zeros and we got our 4 bits)
What if we need the most significant bits?
we apply the same idea, but now the mask will change, according to the bits we need: 11001101 & 11110000 = 11000000 (205 & 0xf0 = 192)
whoops... we got 4 zeros.
How can you get rid of that? Shifting to the right with 4 positions.
so 11000000 >> 4 = 1100 (most significant 4 bits)
I hope this example will help you to get a better understanding of bitwise operations.
One simple solution could be
bit0 = (x & 0xff000000) >> 24;
bit1 = (x & 0x00ff0000) >> 16;
bit2 = (x & 0x0000ff00) >> 8;
bit3 = (x & 0x000000ff);
(bit0 is MSB).

Masking isn't quite turning bits "on" or "off". It is a way to extract only the bits you want from the variable you are using. Lets say that you have the binary number 10011011 and you want the value of the rightmost 4 bits. To do this, you construct another binary number of the same length where there are 0's in the places that you don't want and 1's in the places that you do. Therefore, our binary number is 00001111. You then bitwise AND them together:
1 & 0 = 0
0 & 0 = 0
0 & 0 = 0
1 & 0 = 0
1 & 1 = 1
0 & 1 = 0
1 & 1 = 1
1 & 1 = 1
In java, using hex instead of binary since java doesn't have binary literals, this looks like
int result = 0x9B & 0x0F;
//result is 0xB (or 11 in decimal)
Bit shifting is just what it sounds like. If you have 10011111 and shift it right 2 bits you get 00100111. In java a bit shift of 2 looks like
int result = 0x9B >> 2;
For your program the idea is this:
Mask the rightmost byte of your integer
Shift integer right 8 bits
Repeat three more times

Translating this java implementation of Sieve of Eratosthenes?

This is a program in Java which implements the Sieve or Eratosthenes by storing the array of booleans as an array of bits. I have never coded in Java before, but the general idea is easy to understand. However, I cannot understand how the getBit and setBit functions work? I am guessing that the getBit function creates a bitmask with the bit i set to 1 and does bitwise AND between the mask and the array? However, I'm not really understanding the details (eg. why i is right shifted by 4 before being passed as index to array, and why MEMORY_SIZE is equal to MAX right shifted by 4). Please explain the each step of getBit and setBit in words, and if possible an equivalent implementation in Python?
private static final long MAX = 1000000000L;
private static final long SQRT_MAX = (long) Math.sqrt(MAX) + 1;
private static final int MEMORY_SIZE = (int) (MAX >> 4);
private static byte[] array = new byte[MEMORY_SIZE];
//--//
for (long i = 3; i < SQRT_MAX; i += 2) {
if (!getBit(i)) {
long j = (i * i);
while (j < MAX) {
setBit(j);
j += (2 * i);
}
}
}
//--//
public static boolean getBit(long i) {
byte block = array[(int) (i >> 4)];
byte mask = (byte) (1 << ((i >> 1) & 7));
return ((block & mask) != 0);
}
public static void setBit(long i) {
int index = (int) (i >> 4);
byte block = array[index];
byte mask = (byte) (1 << ((i >> 1) & 7));
array[index] = (byte) (block | mask);
}

Some notes in advance:
(i >> 4) divides i by 16, which is the index of the block (of 8 bits) in array that contains the i-th bit
(i >> 1) divides i by 2
7 in binary code is 111
((i >> 1) & 7) means "the three rightmost bits of i / 2", which is a number between 0 and 7 (inclusive)
(1 << ((i >> 1) & 7)) is a bit shifted to the left between 0 and 7 times (00000001, 00000010, ..., 10000000). This is the bit mask to set/get the bit of interest from the selected block.
getBit(i) explained
First line selects the 8-bit-block (i.e. a byte) in which the bit of interest is located.
Second line calculates a bit mask with exactly one bit set. The position of the set bit is the same as the one of the bit of interest within the 8-bit-block.
Third line extracts the bit of interest using an bitwise AND, returning true if this bit is 1.
setBit(i) explained
Calculation of the 8-bit-block and the bit mask is equivalent to getBit
The difference is that a bitwise OR is used to set the bit of interest.
Edit
To your first question:
It almost makes sense now, can you please explain why we are able to find the position of the bit cooresponding to the number i by shifting a bit left ((i >> 1) & 7) times? In other words, i understand what the operation is doing, but why does this give us the correct bit position?
I think this is because of the optimized nature of the algorithm. Since i is incremented in steps of 2, it is sufficient to use half of the bits (since the others would be set anyway). Thus, i can be divided by 2 to calculate the number of necessary bit shifts.
Regarding your second question:
Also, just to clarify, the reason we increment j by 2*i after each call to setBit is because we only need to set the bits cooresponding to odd multiples of i, right?
Yes, because according to https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes:
Another refinement is to initially list odd numbers only, (3, 5, ..., n), and count in increments of 2p in step 3, thus marking only odd multiples of p.
Your algorithm starts with 3, increments i by 2, and counts in increments of 2*i.
I hope this helps!

How can I extract a particular bit in Java?

I need a specific bit in a byte value stored as int value. My code is as shown below.
private int getBitValue(int byteVal, int bitShift){
byteVal = byteVal << bitShift;
int bit = (int) (byteVal >>>7);
return bit;
}
It is working when I give the bitshift as 1 but when I give the bitshift as 2 and the byteVal as 67(01000011 in binary), I get the value of 'byteVal' as 268 while 'byteVal' should be 3(000011 in binary) after the first line in the method(the left shift). What am I doing wrong here?

For some reason when I try your code I don't get what you get. For your example, if you say byteVal = 0b01000011 and bitShift = 2, then this is what I get:
byteVal = 0b01000011 << 2 = 0b0100001100
bit = (int) (0b0100001100 >>> 7) = (int) (0b010) // redundant cast
returned value: 0b010 == 2
I believe what you intended to do was shift the bit you wanted to the leftmost position, and then shift it all the way to the right to get the bit. However, your code won't do that for a few reasons:
You need to shift left by (variable length - bitShift) to get the desired bit to the place you want. So in this case, what you really want is to shift byteVal left by 6 places, not 2.
int variables are 32 bits wide, not 8. (so you actually want to shift byteVal left by 30 places)
In addition, your question appears to be somewhat contradictory. You state you want a specific bit, yet your example implies you want the bitShift-th least significant bits.
An easier way of getting a specific bit might be to simply shift right as far as you need and then mask with 1: (also, you can't use return with void, but I'm assuming that was a typo)
private int getBitValue(int byteVal, int bitShift) {
byteVal = byteVal >> bitShift; // makes the bitShift-th bit the rightmost bit
// Assumes bit numbers are 0-based (i.e. original rightmost bit is the 0th bit)
return (int) (byteVal & 1) // AND the result with 1, which keeps only the rightmost bit
}
If you want the bitShift-th least significant bits, I believe something like this would work:
private int getNthLSBits(int byteVal, int numBits) {
return byteVal & ((1 << numBits) - 1);
// ((1 << numBits) - 1) gives you numBits ones
// i.e. if numBits = 3, (1 << numBits) - 1 == 0b111
// AND that with byteVal to get the numBits-th least significant bits
}

I'm curious why the answer should be 3 and I think we need more information on what the function should do.
Assuming you want the value of the byteVal's lowest bitShift bits, I'd do the following.
private int getBitValue(int byteVal, int bitShift){
int mask = 1 << bitShift; // mask = 1000.... (number of 0's = bitShift)
mask--; // mask = 000011111 (number of 1's = bitShift)
return (byteVal & mask);
}
At the very least, this function will return 1 for getBitValue(67, 1) and 3 for getBitValue(67,2).

Restricting Binary Output to 8 bits or 4 bits

Here is my FIRST Question
Here is my code:
public class Bits{
public static void main(String args[]){
int i = 2 , j = 4;
int allOnes = ~0;
int left = allOnes << (j+1);
System.out.println("Binary Equivalent at this stage: " +Integer.toBinaryString(left));
}
}
The following is the output I'm getting:
Binary Equivalent at this stage: 11111111111111111111111111100000
How can I restrict it to only 8 bits from the right hand side. I mean 11100000 .
Please explain.
Here is my SECOND Question:
Also, I have one more Question which is totally different with the above one:
public static void main(String args[]){
int i = 2 , j = 4;
int allOnes = ~0; // will equal sequence of all 1s
int left = allOnes << (j+1);
System.out.println("Binary Equivalent at this stage: " +Integer.toBinaryString(left));
}
}
Since I didn't understand the following line:
int allOnes = ~0; // will equal sequence of all 1s
When I tried to output the value of "allOnes" then I got "-1" as my output.
I'm having hard time understanding the very next line which is as follows:
int left = allOnes << (j+1);

int allOnes = ~0;
Takes the integer 0 and applies the NOT operation bitwise so it will have all ones in its binary representation. Intagers use the two's complement format, meaning that a value of a word having all bits as one is value of -1.

If you only care about byte boundaries, then use a ByteBuffer
byte lastByte = ByteBuffer.allocate(4).putInt(i).array()[3];
To restrict this byte to the first four or last four bits, use lastByte & 0b11110000 or lastByte & 0b00001111
The integer representation of -1 is all 1's, i.e. 32 bits all set to 1. You can think of the first bit as -2^31 (note the negative sign), and of each subsequent bit as 2^30, 2^29, etc. Adding 2^0 + 2^1 + 2^2 ... + 2^30 - 2^31 = -1.
I suggest reading this tutorial on bitwise operations.

For #1 Integer.toBinaryString(left) is printing 32 bits (length of Integer), so if you just want the right 8 you can do the following:
Integer.toBinaryString(left).substring(24)
The ~ operator in Java inverts the the bit pattern. Thus 0 turns into ffff.
The << operator shifts the bits by x. You are shifting the bits to the left by 5 so you end up with 5 zeros on the right.
Here are all the bitwise operators for Java

First, a more general solution for the first question than what I've seen so far is
left &= (2 ^ n) - 1;
where n is the number of binary digits that you want to take from the right. This is based around the bitwise AND operator, &, which compares corresponding bits in two numbers and outputs a 1 if they are both 1s and 0 otherwise. For example:
10011001 & 11110000 == 10010000; // true
This is used to create what are known as bitmasks (http://en.wikipedia.org/wiki/Mask_(computing)). Notice how in this example how the left 4 bits of the first number are copied over to the result and how those same 4 bits are all ones in the second number? That's the idea in a bit mask.
So in your case, let's look at n = 8
left &= (2 ^ 8) - 1;
left &= 256 - 1;
left &= 255; // Note that &=, like += or *=, just means left = left & 255
// Also, 255 is 11111111 in binary so it can be used as the bitmask for
// the 8 rightmost bits.
Integer.toBinaryString(left) = "11100000";
Your second question is much more in depth, but you'd probably benefit most from reading the Wikipedia article (http://en.wikipedia.org/wiki/Two's_complement) instead of trying to understand a brief explanation here.

8 bits in decimal has a maximum value of 255. You can use the modulo (remainder) division operator to limit it to 8 bits at this point. For isntance:
int yournum = 35928304284 % 256;
will limit yournum to 8 bits of length. Additionally, as suggested in the comments, you can do this:
int yournum = 3598249230 & 255;
This works as well, and is actually preferred in this case, because it is much faster. The bitwise and function returns 1 if both associated bits are 1; since only the last 8 bits of 255 are one, the integer is implicitly limited to 255.
To answer your second question: A tilde is the bitwise inversion operator. Thus,
int allOnes = ~0;
creates an integer of all 1s. Because of the way twos complements works, that number actually represents -1.

Obtain a specific subset of bits of an int in Java

How would I obtain a specific subset, say bits 5-10, of an int in Java?
Looking for a method where one can pass in specific bit positions. I'm not sure how I would create a mask that changes given the input, or even if that is how one should go about doing it.
I know this is how one would get the front say 10 bits of an int: (I think)
int x = num >> 22;

Say you have a number n, and want bits from i to j (i=5, j=10).
Note, that i=0 will give you the last bit
int value = n & (((1 << (j-i)) - 1) << i );
will give you the result.
The left part is obvious: you have a value, and you will put a bitmask on it.
The value of the mask is ((1 << (j-i)) - 1) << i. It says:
Take a 1 bit (value: 0000000000000001)
Shift it left j-i times (value: 2^(10-5) = 2^5 = 32 = 0000000000100000)
Deduct 1 (value: 31 = 0000000000011111) - have you seen the lowest bits reversed?
Shift it left i times (value: 31*32=992 = 0000001111100000)
So, you have got the bitmask for bits 5 - 10 (more precisely, from 5 to 9, since 10th is not included).

To obtain value of bit 1 (bits are indexed from 0 to 31)
int val = bits & 0x002;
To obtain value of bit 16
int val = bits & (1<<16);
To obtain value of bit n
int val = bits & (1<<n);