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How does cast in java work? [duplicate]

int i =132;
byte b =(byte)i; System.out.println(b);
Mindboggling. Why is the output -124?

In Java, an int is 32 bits. A byte is 8 bits .
Most primitive types in Java are signed, and byte, short, int, and long are encoded in two's complement. (The char type is unsigned, and the concept of a sign is not applicable to boolean.)
In this number scheme the most significant bit specifies the sign of the number. If more bits are needed, the most significant bit ("MSB") is simply copied to the new MSB.
So if you have byte 255: 11111111
and you want to represent it as an int (32 bits) you simply copy the 1 to the left 24 times.
Now, one way to read a negative two's complement number is to start with the least significant bit, move left until you find the first 1, then invert every bit afterwards. The resulting number is the positive version of that number
For example: 11111111 goes to 00000001 = -1. This is what Java will display as the value.
What you probably want to do is know the unsigned value of the byte.
You can accomplish this with a bitmask that deletes everything but the least significant 8 bits. (0xff)
So:
byte signedByte = -1;
int unsignedByte = signedByte & (0xff);
System.out.println("Signed: " + signedByte + " Unsigned: " + unsignedByte);
Would print out: "Signed: -1 Unsigned: 255"
What's actually happening here?
We are using bitwise AND to mask all of the extraneous sign bits (the 1's to the left of the least significant 8 bits.)
When an int is converted into a byte, Java chops-off the left-most 24 bits
1111111111111111111111111010101
&
0000000000000000000000001111111
=
0000000000000000000000001010101
Since the 32nd bit is now the sign bit instead of the 8th bit (and we set the sign bit to 0 which is positive), the original 8 bits from the byte are read by Java as a positive value.

132 in digits (base 10) is 1000_0100 in bits (base 2) and Java stores int in 32 bits:
0000_0000_0000_0000_0000_0000_1000_0100
Algorithm for int-to-byte is left-truncate; Algorithm for System.out.println is two's-complement (Two's-complement is if leftmost bit is 1, interpret as negative one's-complement (invert bits) minus-one.); Thus System.out.println(int-to-byte( )) is:
interpret-as( if-leftmost-bit-is-1[ negative(invert-bits(minus-one(] left-truncate(0000_0000_0000_0000_0000_0000_1000_0100) [)))] )
=interpret-as( if-leftmost-bit-is-1[ negative(invert-bits(minus-one(] 1000_0100 [)))] )
=interpret-as(negative(invert-bits(minus-one(1000_0100))))
=interpret-as(negative(invert-bits(1000_0011)))
=interpret-as(negative(0111_1100))
=interpret-as(negative(124))
=interpret-as(-124)
=-124 Tada!!!

byte in Java is signed, so it has a range -2^7 to 2^7-1 - ie, -128 to 127.
Since 132 is above 127, you end up wrapping around to 132-256=-124. That is, essentially 256 (2^8) is added or subtracted until it falls into range.
For more information, you may want to read up on two's complement.

132 is outside the range of a byte which is -128 to 127 (Byte.MIN_VALUE to Byte.MAX_VALUE)
Instead the top bit of the 8-bit value is treated as the signed which indicates it is negative in this case. So the number is 132 - 256 = -124.

here is a very mechanical method without the distracting theories:
Convert the number into binary representation (use a calculator ok?)
Only copy the rightmost 8 bits (LSB) and discard the rest.
From the result of step#2, if the leftmost bit is 0, then use a calculator to convert the number to decimal. This is your answer.
Else (if the leftmost bit is 1) your answer is negative. Leave all rightmost zeros and the first non-zero bit unchanged. And reversed the rest, that is, replace 1's by 0's and 0's by 1's. Then use a calculator to convert to decimal and append a negative sign to indicate the value is negative.
This more practical method is in accordance to the much theoretical answers above. So, those still reading those Java books saying to use modulo, this is definitely wrong since the 4 steps I outlined above is definitely not a modulo operation.

Two's complement Equation:
In Java, byte (N=8) and int (N=32) are represented by the 2s-complement shown above.
From the equation, a7 is negative for byte but positive for int.
coef: a7 a6 a5 a4 a3 a2 a1 a0
Binary: 1 0 0 0 0 1 0 0
----------------------------------------------
int: 128 + 0 + 0 + 0 + 0 + 4 + 0 + 0 = 132
byte: -128 + 0 + 0 + 0 + 0 + 4 + 0 + 0 = -124

often in books you will find the explanation of casting from int to byte as being performed by modulus division. this is not strictly correct as shown below
what actually happens is the 24 most significant bits from the binary value of the int number are discarded leaving confusion if the remaining leftmost bit is set which designates the number as negative
public class castingsample{
public static void main(String args[]){
int i;
byte y;
i = 1024;
for(i = 1024; i > 0; i-- ){
y = (byte)i;
System.out.print(i + " mod 128 = " + i%128 + " also ");
System.out.println(i + " cast to byte " + " = " + y);
}
}
}

A quick algorithm that simulates the way that it work is the following:
public int toByte(int number) {
int tmp = number & 0xff
return (tmp & 0x80) == 0 ? tmp : tmp - 256;
}
How this work ? Look to daixtr answer. A implementation of exact algorithm discribed in his answer is the following:
public static int toByte(int number) {
int tmp = number & 0xff;
if ((tmp & 0x80) == 0x80) {
int bit = 1;
int mask = 0;
for(;;) {
mask |= bit;
if ((tmp & bit) == 0) {
bit <<=1;
continue;
}
int left = tmp & (~mask);
int right = tmp & mask;
left = ~left;
left &= (~mask);
tmp = left | right;
tmp = -(tmp & 0xff);
break;
}
}
return tmp;
}

If you want to understand this mathematically, like how this works
so basically numbers b/w -128 to 127 will be written same as their decimal value, above that its (your number - 256).
eg. 132, the answer will be
132 - 256 = - 124
i.e.
256 + your answer in the number
256 + (-124) is 132
Another Example
double a = 295.04;
int b = 300;
byte c = (byte) a;
byte d = (byte) b; System.out.println(c + " " + d);
the Output will be 39 44
(295 - 256) (300 - 256)
NOTE: it won't consider numbers after the decimal.

Conceptually, repeated subtractions of 256 are made to your number, until it is in the range -128 to +127. So in your case, you start with 132, then end up with -124 in one step.
Computationally, this corresponds to extracting the 8 least significant bits from your original number. (And note that the most significant bit of these 8 becomes the sign bit.)
Note that in other languages this behaviour is not defined (e.g. C and C++).

In java int takes 4 bytes=4x8=32 bits
byte = 8 bits range=-128 to 127
converting 'int' into 'byte' is like fitting big object into small box
if sign in -ve takes 2's complement
example 1: let number be 130
step 1:130 interms of bits =1000 0010
step 2:condider 1st 7 bits and 8th bit is sign(1=-ve and =+ve)
step 3:convert 1st 7 bits to 2's compliment
000 0010
-------------
111 1101
add 1
-------------
111 1110 =126
step 4:8th bit is "1" hence the sign is -ve
step 5:byte of 130=-126
Example2: let number be 500
step 1:500 interms of bits 0001 1111 0100
step 2:consider 1st 7 bits =111 0100
step 3: the remained bits are '11' gives -ve sign
step 4: take 2's compliment
111 0100
-------------
000 1011
add 1
-------------
000 1100 =12
step 5:byte of 500=-12
example 3: number=300
300=1 0010 1100
1st 7 bits =010 1100
remaining bit is '0' sign =+ve need not take 2's compliment for +ve sign
hence 010 1100 =44
byte(300) =44

N is input number
case 1: 0<=N<=127 answer=N;
case 2: 128<=N<=256 answer=N-256
case 3: N>256
temp1=N/256;
temp2=N-temp*256;
if temp2<=127 then answer=temp2;
else if temp2>=128 then answer=temp2-256;
case 4: negative number input
do same procedure.just change the sign of the solution

Getting value from MSB of 16 bit register

I have 16 bits register which contain some values in LSB and MSB:
LSB:
At bit 0...1 the value is 0
At bit 2 the values is 0
MBS:
At MSB I need to write value 20
So the value that should be written in register is 0 + 0 + 20 = 160
When I'm reading register the I'm doing it on this way:
for the 1st value in bit [0...1]:
firstVal = (valFromReg & (((1 << 2)-1) << 1) / 2)
secondVal = (valFromReg & 4) / 4
But how to read/convert the third value to get number 20?

In Java, a short is a (signed) 16-bit value. You want to split that into 3 values:
Value a is a 2-bit value in bits 0-1
Value b is a 1-bit value in bit 2
Value c is a 13-bit value in bits 3-15
Bit-wise, that can be represented like this: cccc cccc cccc cbaa
To extract the 3 values from the 16-bit reg value, you'd do this:
short reg = /*register value*/;
int a = reg & 0x0003;
int b = (reg >> 2) & 0x0001;
int c = (reg >> 3) & 0x1fff;
To go the other way, you'd do this:
short reg = (short)((c << 3) | (b << 2) | a);
This of course assumes that the values are within value range, i.e. a = 0-3, b = 0-1, and c = 0-8191.

Some things in the question are not quite clear for me...
like:
At MSB I need to write value 20
back in my times MSB was only 1 bit and was only possible to write true or false...
anyways...
A 16 bits signal fits pretty good in an integer...
so you could basically get that register and manipulate it as an integer, then representing that as a binary number AS STRING will lets you to get the MSB or even the bit at any wanted position...
Do this:
Example
int register = -128;
String foo = String.format("%16s", Integer.toBinaryString(register)).replace(' ', '0');
System.out.println(register);
System.out.println(foo);
System.out.println(foo.charAt(0)); //char at 0 is the MSB....

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

Big O of while loop

I have some code here that where x grows like big O(n), however I'm not sure why. It seems more of a logarithmic big O. Could I get some help figuring out why it grows like big O(n)? Thanks!
i = k; x = 1.0;
while (i > 1 ) {
i = (int) Math.floor( i / 2.0 );
x = x *2 ;

Complexity analysis has little to do with what value ends up in a variable, it a property of an algorithm, simplistically (for time complexity) how many steps it needs to do based on some input value.
In this case, given the input value k, your complexity is O(log N) because the division by two "halves the remaining solution space" on each iteration, along the lines of:
i = 128 64 32 16 8 4 2 1
The growth of the variable x which, as mentioned, has nothing to do with the algorithmic complexity, is to double each time through the loop.
So, you have a loop controlled by a value that halves on each iteration. And you have a variable that doubles on each iteration:
i = 128 64 32 16 8 4 2 1
x = 1 2 4 8 16 32 64 128
Hence it makes sense that the relationship between the input value and the final variable value will be a linear one, as shown by the equivalent Python code:
ctrl = 1024
other = 1
while ctrl > 0:
print('{0:4d} {1:4d}'.format(ctrl, other))
ctrl = ctrl // 2
other = other * 2
which outputs:
1024 1
512 2
256 4
128 8
64 16
32 32
16 64
8 128
4 256
2 512
1 1024
Note there that, though the final value in other is 1024, only ten "steps" were executed, since log21024 is 10.

If you're looking to optimize the problem, it looks like you're just calculating the largest bit
This can also be achieved a bit more efficiently with Integer.highestOneBit(int i)
Which is defined as
public static int highestOneBit(int i) {
// HD, Figure 3-1
i |= (i >> 1);
i |= (i >> 2);
i |= (i >> 4);
i |= (i >> 8);
i |= (i >> 16);
return i - (i >>> 1);
}
and should be running in constant time (O(1)) since it is only bit operators
How it works is by shifting the bits down while ORing it with itself, causing all of the bits past the largest to become 1, then to isolate the largest it subtracts that number shifted over to remove all the trailing 1s

new to java - trying to understand: checker |= (1 << val)

the following code will check to see if you have any duplicate characters in the string, but i don't understand the if clause:
public static boolean isUniqueChars(String str) {
int checker = 0;
for (int i = 0; i < str.length(); ++i) {
int val = str.charAt(i) - 'a';
if ((checker & (1 << val)) > 0)
return false;
checker |= (1 << val);
}
return true;
}
I tried to look up some references, I am new to bit shifting, all i understand is that << shifts the binary number left or right. Can you explain to me how checker |= (1 << val) works ? and that 'if' statement as well.

I was also going through this book Cracking the Code Interview and ended up googling for a clear explanations. Finally I understood the concept.
Here is the approach.
Note :
We will assume, in the below code, that the string is only lower case ‘a’ through ‘z’. This will allow us to use just a single int.
Java integer is of size 32
Number of lower case alphabets is 26
So we can clearly set 0/1 (true or false) value inside one integer in
decimal notation.
It is similar to bool visited[32] .
bool uses 1 byte. Hence you need 32 bytes for storing bool visited[32].
Bit masking is a space optimization to this.
Lets start :
You are looping through all the characters in the string.
Suppose on i'th iteration you found character 'b' .
You calculate its 0 based index.
int val = str.charAt(i) - 'a';
For 'b' it is 1. ie 98-97 .
Now using left shift operator, we find the value of 2^1 => 2.
(1 << val) // 1<<1 => 10(binary)
Now let us see how bitwise & works
0 & 0 -> 0
0 & 1 -> 0
1 & 0 -> 0
1 & 1 -> 1
So by the below code :
(checker & (1 << val))
We check if the checker[val] == 0 .
Suppose we had already encountered 'b'.
check = 0000 0000 0000 0000 0000 1000 1000 0010 &
'b' = 0000 0000 0000 0000 0000 0000 0000 0010
----------------------------------------------
result= 0000 0000 0000 0000 0000 0000 0000 0010
ie decimal value = 2 which is >0
So you finally we understood this part.
if ((checker & (1 << val)) > 0)
return false;
Now if 'b' was not encountered, then we set the second bit of checker using bitwise OR.
( This part is called as bit masking. )
OR's Truth table
0 | 0 -> 0
0 | 1 -> 1
1 | 0 -> 1
1 | 1 -> 1
So
check = 0000 0000 0000 0000 0000 1000 1000 0000 |
'b' = 0000 0000 0000 0000 0000 0000 0000 0010
----------------------------------------------
result= 0000 0000 0000 0000 0000 1000 1000 0010
So that simplifies this part:
checker |= (1 << val); // checker = checker | (1 << val);
I hope this helped someone !

Seems like I am late to the party, but let me take a stab at the explanation.
First of all the AND i.e & operation:
0 & 0 = 0
1 & 0 = 0
0 & 1 = 0
1 & 1 = 1
So basically, if you are given a bit, and you want to find out if its 1 or 0, you just & it with a 1. If the result is 1 then you had a 1, else you had 0. We will use this property of the & below.
The OR i.e | operation
0 | 0 = 0
1 | 0 = 1
0 | 1 = 1
1 | 1 = 1
So basically, if you are given a bit, and you want to do something to it so that the output is always 1, then you do an | 1 with it.
Now, In Java the type int is 4 bytes i.e. 32 bits. Thus we can use an int itself as a data-structure to store 32 states or booleans in simpler terms, since a bit can either be 0 or 1 i.e false or true. Since we assume that our string is composed of only lower case characters, we have enough space inside our int to store a boolean for each of the 26 chars!
So first we initialize our data-structure that we call checker to 0 which is nothing but 32 zeros: 0000000000000000000000.
So far so good?
Now we go through our string, for each character, first we get an integer representation of the character.
int val = str.charAt(i) - 'a';
We subtract a from it because we want our integer to be 0 based. So if vals:
a = 0 i.e. `0000000000000000000000`
b = 1 i.e. `0000000000000000000001`
c = 2 i.e. `0000000000000000000010`
d = 4 i.e. `0000000000000000000100`
Now as seen above, a is 32 zeros, but rest of the characters have a single 1 and 31 zeros. So when we use these characters, we left shift each of them by 1, i.e. (1 << val), so each of them have a single 1 bit, and 31 zero bits:
a = 1 i.e. `0000000000000000000001`
b = 2 i.e. `0000000000000000000010`
c = 4 i.e. `0000000000000000000100`
d = 8 i.e. `0000000000000000001000`
We are done with the setup. Now we do 2 things:
First assume all characters are different. For every char we encounter, we want our datastructure i.e. checker to have 1 for that char. So we use our OR property descrived above to generate a 1 in our datastructure, and hence we do:
checker = checker | (1 << val);
Thus checker stores 1 for every character we encounter.
Now we come to the part where characters can repeate. So before we do step 1, we want to make sure that the checker already does not have a 1 at the position corresponding to the current character. So we check the value of
checker & (1 << val)
So with help of the AND property described above, if we get a 1 from this operation, then checker already had a 1 at that position, which means we must have encountered this character before. So we immediately return false.
That's it. If all our & checks return 0, we finally return true, meaning there were no character repititions.

1 << val is the same as 2 to the degree of val. So it's a number which has
just one one in its binary representation (the one is at position val+1, if you count from
the right side of the number to the left one).
a |= b means basically this: set in a all binary flags/ones from the
binary representation of b (and keep those in a which were already set).

The other answers explain the coding operator usages but i don't think they touch the logic behind this code.
Basically the code 1 << val is shifting 1 in a binary number to a unique place for each character for example
a-0001
b-0010
c-0100
d-1000
As you can notice for different characters the place of 1 is different
checker = checker | (1 << val)
checker here is Oring (basically storing 1 at the same place as it was in 1<<val)
So checker knows what characters have already ocurred
Let's say after the occurence of a,b,c,d checker would look like this
0000 1111
finally
if ((checker & (1 << val)) > 0)
checks if that character has already been occured before if yes return false.To explain you should know a little about AND(&) operation.
1&1->1
0&0->0
1&0->0
So checker currently have 1 in places whose corresponding characters have already occured the only way the expression inside if statement is true
if a character occurs twice which leads 1&1->1 > 0

This sets the 'val'th bit from the right to 1.
1 << val is a 1 shifted left val times. The rest of the value is 0.
The line is equivalent to checker = checker | (1 << val). Or-ing with a 0 bit does nothing, since x | 0 == x. But or-ing with 1 always results in 1. So this turns (only) that bit on.
The if statement is similar, in that it is checking to see if the bit is already on. The mask value 1 << val is all 0s except for a single 1. And-ing with 0 always produces 0, so most bits in the result are 0. x & 1 == x, so this will be non-zero only if that bit at val is not 0.

checker |= (1 << val) is the same as checker = checker | (1 << val).
<< is left bit shift as you said. 1 << val means it's a 1 shifted val digits left.
Example: 1 << 4 is 1000. A left bit shift is the same as multiply by 2. 4 left bit shifts are 4 times 1 multiplied by 2.
1 * 2 = 2 (1)
2 * 2 = 4 (2)
4 * 2 = 8 (3)
8 * 2 = 16 = (4)
| operator is bitwise or. It's like normal or for one bit. If we have more than one bit you do the or operation for every bit.
Example:
110 | 011 = 111
You can use that for setting flags (make a bit 1).
The if condition is similar to that, but has the & operator, which is bitwise and. It is mainly used to mask a binary number.
Example:
110 | 100 = 100
So your code just checks if the bit at place val is 1, then return false, otherwise set the bit at place val to 1.

It means do a binary OR on the values checker and (1 << val) (which is 1, left shifted val times) and save the newly created value in checker.
Left Shift (<<)
Shift all the binary digits left one space. Effectively raise the number to 2 to the power of val or multiply the number by 2 val times.
Bitwise OR (|)
In each binary character of both left and right values, if there is a 1 in the place of either of the two numbers then keep it.
Augmented Assignment (|=)
Do the operation (in this case bitwise OR) and assign the value to the left hand variable. This works with many operators such as:-
a += b, add a to b and save the new value in a.
a *= b, multiply a by b and save the new value in a.

Bitwise shift works as follows:
Example: a=15 (bit representation : 0000 1111)
For operation: a<<2
It will rotate bit representation by 2 positions in left direction.
So a<<2 is 0011 1100 = 0*2^7+0*2^6+1*2^5+1*2^4+1*2^3+1*2^2+0*2^1+0*2^0 = 1*2^5+1*2^4+1*2^3+1*2^2 = 32+18+8+4=60
hence a<<2 = 60
Now:
checker & (1<<val),
will always be greater then 0, if 1 is already present at 1<<val position.
Hence we can return false.
Else we will assign checker value of 1 at 1

I've been working on the algorithm and here's what I noticed that would also work. It makes the algorithm easier to understand when you exercise it by hand:
public static boolean isUniqueChars(String str) {
if (str.length() > 26) { // Only 26 characters
return false;
}
int checker = 0;
for (int i = 0; i < str.length(); i++) {
int val = str.charAt(i) - 'a';
int newValue = Math.pow(2, val) // int newValue = 1 << val
if ((checker & newValue) > 0) return false;
checker += newValue // checker |= newValue
}
return true;
When we get the value of val (0-25), we could either shift 1 to the right by the value of val, or we could use the power of 2s.
Also, for as long as the ((checker & newValue) > 0) is false, the new checker value is generated when we sum up the old checker value and the newValue.

public static boolean isUniqueChars(String str) {
int checker = 0;
for (int i = 0; i < str.length(); ++i) {
int val = str.charAt(i) - 'a';
if ((checker & (1 << val)) > 0)
return false;
checker |= (1 << val);
}
return true;
}
1 << val uses right shift operator. Let us say we have character z. ASCII code of z is 122. a-z is 97- 122 = 25. If we multiply 1*(2)^25 = 33554432. Binary of that is 10000000000000000000000000
if checker has 1 on its 26th bit then this statement if ((checker & (1 << val)) > 0) would be true and isUniqueChar would return false.
otherwise checker would turn it's 26th bit on. |= operator(bitwise or and assignment operator) does checker bitwise OR 10000000000000000000000000. Assigns the result to checker.