Develop Reference

Bitwise operator with negative numbers

Why does..
-23&30 = 8
5&-3 = 5
15&-1 = 15
I understand & with positive numbers but for some reason when a negative number is thrown, I don't understand how the answer is derived.

You should read about 2's complement method of representing negative numbers in binary.
For example:
5 == 00000000 00000000 00000000 00000101
&
-3 == 11111111 11111111 11111111 11111101
= -----------------------------------
5 == 00000000 00000000 00000000 00000101

JAVA Bitwise code purpose , &

// following code prints out Letters aA bB cC dD eE ....
class UpCase {
public static void main(String args[]) {
char ch;
for(int i = 0; i < 10; i++) {
ch = (char)('a' + i);
System.out.print(ch);
ch = (char)((int) ch & 66503);
System.out.print(ch + " ")
}
}
}
Still learning Java but struggling to understand bitwise operations. Both codes work but I don't understand the binary reasons behind these codes. Why is (int) casted back to ch and what is 66503 used for that enables it to print out different letter casings.
//following code displays bits within a byte
class Showbits {
public static void main(String args[]) {
int t;
byte val;
val = 123;
for(t = 128; t > 0; t = t/2) {
if((val & t) != 0)
System.out.print("1 ");
else System.out.print("0 ");
}
}
}
//output is 0 1 1 1 1 0 1 1
For this code's output what's the step breakdown to achieve it ? If 123 is 01111011 and 128 as well as 64 and 32 is 10000000 shouldnt the output be 00000000 ? As & turns anything with 0 into a 0 ? Really confused.

Second piece of code(Showbits):
The code is actually converting decimal to binary. The algorithm uses some bit magic, mainly the AND(&) operator.
Consider the number 123 = 01111011 and 128 = 10000000. When we AND them together, we get 0 or a non-zero number depending whether the 1 in 128 is AND-ed with a 1 or a 0.
10000000
& 01111011
----------
00000000
In this case, the answer is a 0 and we have the first bit as 0.
Moving forward, we take 64 = 01000000 and, AND it with 123. Notice the shift of the 1 rightwards.
01000000
& 01111011
----------
01000000
AND-ing with 123 produces a non-zero number this time, and the second bit is 1. This procedure is repeated.
First piece of code(UpCase):
Here 65503 is the negation of 32.
32 = 0000 0000 0010 0000
~32 = 1111 1111 1101 1111
Essentially, we subtract a value of 32 from the lowercase letter by AND-ing with the negation of 32. As we know, subtracting 32 from a lowercase ASCII value character converts it to uppercase.

UpCase
The decimal number 66503 represented by a 32 bit signed integer is 00000000 00000001 00000011 11000111 in binary.
The ASCII letter a represented by a 8 bit char is 01100001 in binary (97 in decimal).
Casting the char to a 32 bit signed integer gives 00000000 00000000 00000000 01100001.
&ing the two integers together gives:
00000000 00000000 00000000 01100001
00000000 00000001 00000011 11000111
===================================
00000000 00000000 00000000 01000001
which casted back to char gives 01000001, which is decimal 65, which is the ASCII letter A.
Showbits
No idea why you think that 128, 64 and 32 are all 10000000. They obviously can't be the same number, since they are, well, different numbers. 10000000 is 128 in decimal.
What the for loop does is start at 128 and go through every consecutive next smallest power of 2: 64, 32, 16, 8, 4, 2 and 1.
These are the following binary numbers:
128: 10000000
64: 01000000
32: 00100000
16: 00010000
8: 00001000
4: 00000100
2: 00000010
1: 00000001
So in each loop it &s the given value together with each of these numbers, printing "0 " when the result is 0, and "1 " otherwise.
Example:
val is 123, which is 01111011.
So the loop will look like this:
128: 10000000 & 01111011 = 00000000 -> prints "0 "
64: 01000000 & 01111011 = 01000000 -> prints "1 "
32: 00100000 & 01111011 = 00100000 -> prints "1 "
16: 00010000 & 01111011 = 00010000 -> prints "1 "
8: 00001000 & 01111011 = 00001000 -> prints "1 "
4: 00000100 & 01111011 = 00000000 -> prints "0 "
2: 00000010 & 01111011 = 00000010 -> prints "1 "
1: 00000001 & 01111011 = 00000001 -> prints "1 "
Thus the final output is "0 1 1 1 1 0 1 1", which is exactly right.

Java8 unsigned arithmetic

Java 8 is widely reported to have library support for unsigned integers. However, there seem to be no articles explaining how to use it and how much is possible.
Some functions like Integer.CompareUnsigned are easy enough to find and seem to do what one would expect. However, I fail to write even a simple loop that loops over all powers of two within the range of unsigned long.
int i = 0;
for(long l=1; (Long.compareUnsigned(l, Long.MAX_VALUE*2) < 0) && i<100; l+=l) {
System.out.println(l);
i++;
}
produces the output
1
2
4
8
...
1152921504606846976
2305843009213693952
4611686018427387904
-9223372036854775808
0
0
0
...
0
Am I missing something or are external libraries still required for this simple task?

If you're referring to
(Long.compareUnsigned(l, Long.MAX_VALUE*2) < 0)
l reaches
-9223372036854775808
unsigned it is
9223372036854775808
and
Long.MAX_VALUE*2
is
18446744073709551614
So l is smaller than Long.MAX_VALUE*2 in the unsigned world.
Assuming you're asking about the 0's
0
0
0
...
0
the problem (if you see it that way) is that, for long (other numerical primitives), the first bit is the sign bit.
so
10000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
is
-9223372036854775808
When you do
-9223372036854775808 + -9223372036854775808
you underflow (overflow?) since
10000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
+ 10000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
is
00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
which is 0. On later loop iterations, 0 + 0 remains 0.

The only problem here is that you're printing l as a signed integer. You can use Integer.toUnsignedString to get the results you're expecting:
int i = 0;
byte[] tmp = new byte[9];
for(int l=1; (Long.compareUnsigned(l, Long.MAX_VALUE*2) < 0) && i<100; l+=l) {
System.out.println(Integer.toUsignedString(l)); // <== MODIFIED THIS LINE
i++;
}

count leading zeros (clz) or number of leading zeros (nlz) in Java

I need int 32 in binary as 00100000 or int 127 in binary 0111 1111.
The variant Integer.toBinaryString returns results only from 1.
If I build the for loop this way:
for (int i= 32; i <= 127; i + +) {
System.out.println (i);
System.out.println (Integer.toBinaryString (i));
}
And from binary numbers I need the number of leading zeros (count leading zeros (clz) or number of leading zeros (nlz)) I really meant the exact number of 0, such ex: at 00100000 -> 2 and at 0111 1111 - > 1

How about
int lz = Integer.numberOfLeadingZeros(i & 0xFF) - 24;
int tz = Integer.numberOfLeadingZeros(i | 0x100); // max is 8.

Count the number of leading zeros as follows:
int lz = 8;
while (i)
{
lz--;
i >>>= 1;
}
Of course, this supposes the number doesn't exceed 255, otherwise, you would get negative results.

Efficient solution is int ans = 8-(log2(x)+1)
you can calculate log2(x)= logy (x) / logy (2)

public class UtilsInt {
int leadingZerosInt(int i) {
return leadingZeros(i,Integer.SIZE);
}
/**
* use recursion to find occurence of first set bit
* rotate right by one bit & adjust complement
* check if rotate value is not zero if so stop counting/recursion
* #param i - integer to check
* #param maxBitsCount - size of type (in this case int)
* if we want to check only for:
* positive values we can set this to Integer.SIZE / 2
* (as int is signed in java - positive values are in L16 bits)
*/
private synchronized int leadingZeros(int i, int maxBitsCount) {
try {
logger.debug("checking if bit: "+ maxBitsCount
+ " is set | " + UtilsInt.intToString(i,8));
return (i >>>= 1) != 0 ? leadingZeros(i, --maxBitsCount) : maxBitsCount;
} finally {
if(i==0) logger.debug("bits in this integer from: " + --maxBitsCount
+ " up to last are not set (i'm counting from msb->lsb)");
}
}
}
test statement:
int leadingZeros = new UtilsInt.leadingZerosInt(255); // 8
test output:
checking if bit: 32 is set |00000000 00000000 00000000 11111111
checking if bit: 31 is set |00000000 00000000 00000000 01111111
checking if bit: 30 is set |00000000 00000000 00000000 00111111
checking if bit: 29 is set |00000000 00000000 00000000 00011111
checking if bit: 28 is set |00000000 00000000 00000000 00001111
checking if bit: 27 is set |00000000 00000000 00000000 00000111
checking if bit: 26 is set |00000000 00000000 00000000 00000011
checking if bit: 25 is set |00000000 00000000 00000000 00000001
bits in this integer from: 24 up to last are not set (i'm counting from msb->lsb)

Bitshifting in Java

I'm trying to understand how bit shift works. Can someone please explain the meaning of this line:
while ((n&1)==0) n >>= 1;
where n is an integer and give me an example of a n when the shift is executed.

Breaking it down:
n & 1 will do a binary comparison between n, and 1 which is 00000000000000000000000000000001 in binary. As such, it will return 00000000000000000000000000000001 when n ends in a 1 (positive odd or negative even number) and 00000000000000000000000000000000 otherwise.
(n & 1) == 0 will hence be true if n is even (or negative odd) and false otherwise.
n >> = 1 is equivalent to n = n >> 1. As such it shifts all bits to the right, which is roughly equivalent to a division by two (rounding down).
If e.g. n started as 12 then in binary it would be 1100. After one loop it will be 110 (6), after another it will be 11 (3) and then the loop will stop.
If n is 0 then after the next loop it will still be 0, and the loop will be infinite.

Lets n be 4 which in binary is represented as:
00000000 00000000 00000000 00000100
(n&1) bitwise ands the n with 1. 1 has the binary representation of:
00000000 00000000 00000000 00000001
The result of the bitwise anding is 0:
00000000 00000000 00000000 00000100 = n
00000000 00000000 00000000 00000001 = 1
------------------------------------
00000000 00000000 00000000 00000000 = 0
so the condition of while is true. Effectively (n&1) was used to extract the least significant bit of the n.
In the while loop you right shift(>>) n by 1. Right shifting a number by k is same as dividing the number by 2^k.
n which is now 00000000 00000000 00000000 00000100 on right shifting once becomes
00000000 00000000 00000000 00000010 which is 2.
Next we extract the LSB(least significant bit) of n again which is 0 and right shift again to give 00000000 00000000 00000000 0000001 which is 1.
Next we again extract LSB of n, which is now 1 and the loop breaks.
So effectively you keep dividing your number n by 2 till it becomes odd as odd numbers have their LSB set.
Also note that if n is 0 to start with you'll go into an infinite loop because no matter how many times you divide 0 by 2 you'll not get a odd number.

Assume n = 12. The bits for this would be 1100 (1*8 + 1*4 + 0*2 + 0*1 = 12).
The first time through the loop n & 1 == 0 because the last digit of 1100 is 0 and when you AND that with 1, you get 0. So n >>= 1 will cause n to change from 1100 (12) to 110 (6). As you may notice, shifting right has the same effect as dividing by 2.
The last bit is still zero, so n & 1 will still be 0, so it will shift right one more time. n>>=1 will cause it to shift one more digit to the right changing n from 110 (6) to 11 (3).
Now you can see the last bit is 1, so n & 1 will be 1, causing the while loop to stop executing. The purpose of the loop appears to be to shift the number to the right until it finds the first turned-on bit (until the result is odd).

Let's assume equals 42 (just because):
int n = 42;
while ((n & 1) == 0) {
n >>= 1;
}
Iteration 0:
n = 42 (or 0000 0000 0000 0000 0000 0000 0010 1010)
n & 1 == 0 is true (because n&1 = 0 or 0000 0000 0000 0000 0000 0000 0000 0000)
Iteration 1:
n = 21 (or 0000 0000 0000 0000 0000 0000 0001 0101)
n & 1 == 0 is false (because n & 1 == 1 or 0000 0000 0000 0000 0000 0000 0000 0001)
What it does:
Basically, you loop divides n by 2 as long as n is an even number:
n & 1 is a simple parity check,
n >>= 1 shifts the bits to the right, which just divides by 2.

for example if n was
n= b11110000
then
n&1= b11110000 &
b00000001
---------
b00000000
n>>=1 b11110000 >> 1
---------
b01111000
n= b01111000
if the loop continues it should be
n= b00001111

n & 1 is actually a bitwise AND operataion. Here the bit pattern of n would be ANDED against the bit pattern of 1. Who's result will be compared against zero. If yes then n is right shifted 1 times. You can take the one right shift as division by 2 and so on.