Develop Reference

Compare bits to a certain integer n in c# [duplicate]

I have do not have much knowledge of C and I'm stuck with a problem since one of my colleague is on leave.
I have a 32 bit number and i have to extract bits from it. I did go through a few threads but I'm still not clear how to do so. I would be highly obliged if someone can help me.
Here is an example of what I need to do:
Assume hex number = 0xD7448EAB.
In binary = 1101 0111 0100 0100 1000 1110 1010 1011.
I need to extract the 16 bits, and output that value. I want bits 10 through 25.
The lower 10 bits (Decimal) are ignored. i.e., 10 1010 1011 are ignored.
And the upper 6 bits (Overflow) are ignored. i.e. 1101 01 are ignored.
The remaining 16 bits of data needs to be the output which is 11 0100 0100 1000 11 (numbers in italics are needed as the output).
This was an example but I will keep getting different hex numbers all the time and I need to extract the same bits as I explained.
How do I solve this?
Thank you.
For this example you would output 1101 0001 0010 0011, which is 0xD123, or 53,539 decimal.

You need masks to get the bits you want. Masks are numbers that you can use to sift through bits in the manner you want (keep bits, delete/clear bits, modify numbers etc). What you need to know are the AND, OR, XOR, NOT, and shifting operations. For what you need, you'll only need a couple.
You know shifting: x << y moves bits from x *y positions to the left*.
How to get x bits set to 1 in order: (1 << x) - 1
How to get x bits set to 1, in order, starting from y to y + x: ((1 << x) -1) << y
The above is your mask for the bits you need. So for example if you want 16 bits of 0xD7448EAB, from 10 to 25, you'll need the above, for x = 16 and y = 10.
And now to get the bits you want, just AND your number 0xD7448EAB with the mask above and you'll get the masked 0xD7448EAB with only the bits you want. Later, if you want to go through each one, you'll need to shift your result by 10 to the right and process each bit at a time (at position 0).
The answer may be a bit longer, but it's better design than just hard coding with 0xff or whatever.

OK, here's how I wrote it:
#include <stdint.h>
#include <stdio.h>
main() {
uint32_t in = 0xd7448eab;
uint16_t out = 0;
out = in >> 10; // Shift right 10 bits
out &= 0xffff; // Only lower 16 bits
printf("%x\n",out);
}
The in >> 10 shifts the number right 10 bits; the & 0xffff discards all bits except the lower 16 bits.

I want bits 10 through 25.
You can do this:
unsigned int number = 0xD7448EAB;
unsigned int value = (number & 0x3FFFC00) >> 10;
Or this:
unsigned int number = 0xD7448EAB;
unsigned int value = (number >> 10) & 0xFFFF;

I combined the top 2 answers above to write a C program that extracts the bits for any range of bits (not just 10 through 25) of a 32-bit unsigned int. The way the function works is that it returns bits lo to hi (inclusive) of num.
#include <stdio.h>
#include <stdint.h>
unsigned extract(unsigned num, unsigned hi, unsigned lo) {
uint32_t range = (hi - lo + 1); //number of bits to be extracted
//shifting a number by the number of bits it has produces inconsistent
//results across machines so we need a special case for extract(num, 31, 0)
if(range == 32)
return num;
uint32_t result = 0;
//following the rule above, ((1 << x) - 1) << y) makes the mask:
uint32_t mask = ((1 << range) -1) << lo;
//AND num and mask to get only the bits in our range
result = num & mask;
result = result >> lo; //gets rid of trailing 0s
return result;
}
int main() {
unsigned int num = 0xd7448eab;
printf("0x%x\n", extract(num, 10, 25));
}

Merge first n bits of a byte with last 8-n bits of another byte

How can I merge first n bits of a byte with last 8-n bits of another byte?
I know something like below for picking 3 bits from first and 5 from second (Which I have observed in DES encryption algorithm)
zByte=(xByte & 0xE0) | (yByte & 0x1F); But I don't know maths behind why we need to use 0XE0 and 0X1F in this case. So I am trying to understand the details with regards to each bit.

In C#, that would be something like:
int mask = ~((-1) << n);
var result = (x & ~mask) | (y & mask);
i.e. we build a mask that is (for n = 5) : 000....0011111, then we combine (&) one operand with that mask, the other operand with the inverse (~) of the mask, and compose them (|).
You could also probably do something more quickly just using shift operations (avoiding a mask completely) - but only if the data can be treated as unsigned (so Java might struggle here).

It just sounds like you don't understand how boolean arithmetic works? If this is your question it works like this:
0xEO and 0x1F are hexidecimal representations of numbers. If we convert these numbers to binary they would be:
0xE0 = 11100000
0x1F = 00011111
Additionally & (and) and | (or) are bitwise logical operators. To understand logical operators, first remember the 1 = true and 0 = false.
The truth table for & is:
0 & 0 = 0
0 & 1 = 0
1 & 0 = 0
1 & 1 = 1
The truth table for | is:
0 | 0 = 0
0 | 1 = 1
1 | 0 = 1
1 | 1 = 1
So let's breakdown your equation piece by piece. First we will evaluate the code in parenthesis first. We will walk through each number in binary and for the & operator if each operand has a 1 in the same bit position we will return 1. If either number has a 0 then we will return 0. After we finish the evaluation of the operands in the parenthesis we will then take the 2 resulting numbers and apply the | operator bit by bit. If either number has a 1 in the same bit position we will return 1. If both numbers have a 0 in the same bit position we will return 0.
For the sake of discussion, let's say that
xByte = 255 or (FF in hex and 11111111 in binary)
yByte = 0 or (00 in hex and 00000000 in binary)
When you apply the & and | operators we are going to compare each bit one at a time:
zByte = (xByte & 0xEO) | (yByte & 0x1F)
becomes:
zByte = (11111111 & 11100000) | (00000000 & 00011111)
zByte = 111000000 | 00000000
zByte = 11100000
If you understand this and how boolean logic works then you can use Marc Gravell's answer.

The math behind those numbers (0xE0 and 0x1F) is quite simple. First we are exploiting the fact that 0 & <bit> always equals 0 and 1 & <bit> always equals <bit>.
0x1F is 00011111 binary, which means that the first 3 bits will always be 0 after an & operation with another byte - and the last 5 bits will be the same they were in the other byte. Remember that every 1 in a binary number represents a power of 2, so if you want to find the mask mathematically it would be the sum of 2^x from x = 0 to n-1. Then you can find the opposite mask (the one that is 11100000) to extract the first 3 bit, you simply need to subtract the mask from 11111111, and you will get 11100000 (0xE0).

In java,
By using the following function we can get the first n bits of the first Byte and last 8 n bits of the second byte.
public class BitExample {
public static void main(String[] args) {
Byte a = 15;
Byte b = 16;
String mergedValue=merge(4, a, b);
System.out.println(mergedValue);
}
public static String merge(int n, Byte a, Byte b) {
String mergedString = "";
String sa = Integer.toBinaryString(a);
String sb = Integer.toBinaryString(b);
if(n>sa.length()) {
for(int i=0; i<(n-sa.length()); i++) {
mergedString+="0";
}
mergedString+=sa;
}else{
mergedString+=sa.substring(0, n);
}
if(8*n>sb.length()) {
for(int i=0; i<(8*n-sb.length()); i++) {
mergedString+="0";
}
mergedString+=sb;
}
return mergedString;
}
}

bitwise shift in uint

uint number = 0x418 in bits : 0000010000011000
uint number1 = 0x8041 in bits: 1000000001000001
uint number2 = 0x1804 in bits: 0001100000000100
I cannot get 0x8041 with
number >> 4;
or
(number >> 4) & 0xffff;
How I can get 0x8041 and 0x1804 from 0x418 with shift?
SOLUTION
(number >> nbits) | (number << (16 - nbits))

C# does not have a bitwise rotate operator - bits shifted past the right end just fall off and vanish. What you can do to solve this is
(number >> nbits) | (number << (32 - nbits))
which will right-rotate a 32-bit unsigned integer by nbits bits.

What you are describing is typically known as Rotation, not Shifting. In assembly (x86), this is exposed via ROR and ROL instructions.
I'm not aware of a bitwise operator available in C# to do this, but the algorithm is simple enough:
value = value & 0x1 ? (1 << Marshal.SizeOf(value) * 8 - 1) | (value >> 1) : ( value >> 1);

Number of unset bit left of most significant set bit?

Assuming the 64bit integer 0x000000000000FFFF which would be represented as
00000000 00000000 00000000 00000000
00000000 00000000 >11111111 11111111
How do I find the amount of unset bits to the left of the most significant set bit (the one marked with >) ?

In straight C (long long are 64 bit on my setup), taken from similar Java implementations: (updated after a little more reading on Hamming weight)
A little more explanation: The top part just sets all bit to the right of the most significant 1, and then negates it. (i.e. all the 0's to the 'left' of the most significant 1 are now 1's and everything else is 0).
Then I used a Hamming Weight implementation to count the bits.
unsigned long long i = 0x0000000000000000LLU;
i |= i >> 1;
i |= i >> 2;
i |= i >> 4;
i |= i >> 8;
i |= i >> 16;
i |= i >> 32;
// Highest bit in input and all lower bits are now set. Invert to set the bits to count.
i=~i;
i -= (i >> 1) & 0x5555555555555555LLU; // each 2 bits now contains a count
i = (i & 0x3333333333333333LLU) + ((i >> 2) & 0x3333333333333333LLU); // each 4 bits now contains a count
i = (i + (i >> 4)) & 0x0f0f0f0f0f0f0f0fLLU; // each 8 bits now contains a count
i *= 0x0101010101010101LLU; // add each byte to all the bytes above it
i >>= 56; // the number of bits
printf("Leading 0's = %lld\n", i);
I'd be curious to see how this was efficiency wise. Tested it with several values though and it seems to work.

Based on: http://www.hackersdelight.org/HDcode/nlz.c.txt
template<typename T> int clz(T v) {int n=sizeof(T)*8;int c=n;while (n){n>>=1;if (v>>n) c-=n,v>>=n;}return c-v;}
If you'd like a version that allows you to keep your lunch down, here you go:
int clz(uint64_t v) {
int n=64,c=64;
while (n) {
n>>=1;
if (v>>n) c-=n,v>>=n;
}
return c-v;
}
As you'll see, you can save cycles on this by careful analysis of the assembler, but the strategy here is not a terrible one. The while loop will operate Lg[64]=6 times; each time it will convert the problem into one of counting the number of leading bits on an integer of half the size.
The if statement inside the while loop asks the question: "can i represent this integer in half as many bits", or analogously, "if i cut this in half, have i lost it?". After the if() payload completes, our number will always be in the lowest n bits.
At the final stage, v is either 0 or 1, and this completes the calculation correctly.

If you are dealing with unsigned integers, you could do this:
#include <math.h>
int numunset(uint64_t number)
{
int nbits = sizeof(uint64_t)*8;
if(number == 0)
return nbits;
int first_set = floor(log2(number));
return nbits - first_set - 1;
}
I don't know how it will compare in performance to the loop and count methods that have already been offered because log2() could be expensive.
Edit:
This could cause some problems with high-valued integers since the log2() function is casting to double and some numerical issues may arise. You could use the log2l() function that works with long double. A better solution would be to use an integer log2() function as in this question.

// clear all bits except the lowest set bit
x &= -x;
// if x==0, add 0, otherwise add x - 1.
// This sets all bits below the one set above to 1.
x+= (-(x==0))&(x - 1);
return 64 - count_bits_set(x);
Where count_bits_set is the fastest version of counting bits you can find. See https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel for various bit counting techniques.

I'm not sure I understood the problem correctly. I think you have a 64bit value and want to find the number of leading zeros in it.
One way would be to find the most significant bit and simply subtract its position from 63 (assuming lowest bit is bit 0). You can find out the most significant bit by testing whether a bit is set from within a loop over all 64 bits.
Another way might be to use the (non-standard) __builtin_clz in gcc.

I agree with the binary search idea. However two points are important here:
The range of valid answers to your question is from 0 to 64 inclusive. In other words - there may be 65 different answers to the question. I think (almost sure) all who posted the "binary search" solution missed this point, hence they'll get wrong answer for either zero or a number with the MSB bit on.
If speed is critical - you may want to avoid the loop. There's an elegant way to achieve this using templates.
The following template stuff finds the MSB correctly of any unsigned type variable.
// helper
template <int bits, typename T>
bool IsBitReached(T x)
{
const T cmp = T(1) << (bits ? (bits-1) : 0);
return (x >= cmp);
}
template <int bits, typename T>
int FindMsbInternal(T x)
{
if (!bits)
return 0;
int ret;
if (IsBitReached<bits>(x))
{
ret = bits;
x >>= bits;
} else
ret = 0;
return ret + FindMsbInternal<bits/2, T>(x);
}
// Main routine
template <typename T>
int FindMsb(T x)
{
const int bits = sizeof(T) * 8;
if (IsBitReached<bits>(x))
return bits;
return FindMsbInternal<bits/2>(x);
}

Here you go, pretty trivial to update as you need for other sizes...
int bits_left(unsigned long long value)
{
static unsigned long long mask = 0x8000000000000000;
int c = 64;
// doh
if (value == 0)
return c;
// check byte by byte to see what has been set
if (value & 0xFF00000000000000)
c = 0;
else if (value & 0x00FF000000000000)
c = 8;
else if (value & 0x0000FF0000000000)
c = 16;
else if (value & 0x000000FF00000000)
c = 24;
else if (value & 0x00000000FF000000)
c = 32;
else if (value & 0x0000000000FF0000)
c = 40;
else if (value & 0x000000000000FF00)
c = 48;
else if (value & 0x00000000000000FF)
c = 56;
// skip
value <<= c;
while(!(value & mask))
{
value <<= 1;
c++;
}
return c;
}

Same idea as user470379's, but counting down ...
Assume all 64 bits are unset. While value is larger than 0 keep shifting the value right and decrementing number of unset bits:
/* untested */
int countunsetbits(uint64_t val) {
int x = 64;
while (val) { x--; val >>= 1; }
return x;
}

Try
int countBits(int value)
{
int result = sizeof(value) * CHAR_BITS; // should be 64
while(value != 0)
{
--result;
value = value >> 1; // Remove bottom bits until all 1 are gone.
}
return result;
}

Use log base 2 to get you the most significant digit which is 1.
log(2) = 1, meaning 0b10 -> 1
log(4) = 2, 5-7 => 2.xx, or 0b100 -> 2
log(8) = 3, 9-15 => 3.xx, 0b1000 -> 3
log(16) = 4 you get the idea
and so on...
The numbers in between become fractions of the log result. So typecasting the value to an int gives you the most significant digit.
Once you get this number, say b, the simple 64 - n will be the answer.
function get_pos_msd(int n){
return int(log2(n))
}
last_zero = 64 - get_pos_msd(n)

Bit manipulation in C# using a mask

I need a little help with bitmap operations in C#
I want to take a UInt16, isolate an arbitrary number of bits, and set them using another UInt16 value.
Example:
10101010 -- Original Value
00001100 -- Mask - Isolates bits 2 and 3
Input Output
00000000 -- 10100010
00000100 -- 10100110
00001000 -- 10101010
00001100 -- 10101110
^^

It seems like you want:
(orig & ~mask) | (input & mask)
The first half zeroes the bits of orig which are in mask. Then you do a bitwise OR against the bits from input that are in mask.

newValue = (originalValue & ~mask) | (inputValue & mask);
originalValue -> 10101010
inputValue -> 00001000
mask -> 00001100
~mask -> 11110011
(originalValue & ~mask)
10101010
& 11110011
----------
10100010
^^
Cleared isolated bits from the original value
(inputValue & mask)
00001000
& 00001100
----------
00001000
newValue =
10100010
| 00001000
----------
10101010

Something like this?
static ushort Transform(ushort value){
return (ushort)(value & 0x0C/*00001100*/ | 0xA2/*10100010*/);
}
This will convert all your sample inputs to your sample outputs. To be more general, you'd want something like this:
static ushort Transform(ushort input, ushort mask, ushort bitsToSet){
return (ushort)(input & mask | bitsToSet & ~mask);
}
And you would call this with:
Transform(input, 0x0C, 0xA2);
For the equivalent behavior of the first function.

A number of the terser solutions here look plausible, especially JS Bangs', but don't forget that you also have a handy BitArray collection to use in the System.Collections namespace: http://msdn.microsoft.com/en-us/library/system.collections.bitarray.aspx

If you want to do bitwise manipulations, I have written a very versatile method to copy any number of bits from one byte (source byte) to another byte (target byte). The bits can be put to another starting bit in the target byte.
In this example, I want to copy 3 bits (bitCount=3) from bit #4 (sourceStartBit) to bit #3 (destinationStartBit). Please note that the numbering of bits starts with "0" and that in my method, the numbering starts with the most significant bit = 0 (reading from left to right).
byte source = 0b10001110;
byte destination = 0b10110001;
byte result = CopyByteIntoByte(source, destination, 4, 1, 3);
Console.WriteLine("The binary result: " + Convert.ToString(result, toBase: 2));
//The binary result: 11110001
byte CopyByteIntoByte(byte sourceByte, byte destinationByte, int sourceStartBit, int destStartBit, int bitCount)
{
int[] mask = { 0, 1, 3, 7, 15, 31, 63, 127, 255 };
byte sourceMask = (byte)(mask[bitCount] << (8 - sourceStartBit - bitCount));
byte destinationMask = (byte)(~(mask[bitCount] << (8-destStartBit - bitCount)));
byte destinationToCopy = (byte)(destinationByte & destinationMask);
int diff = destStartBit - sourceStartBit;
byte sourceToCopy;
if(diff > 0)
{
sourceToCopy = (byte)((sourceByte & sourceMask) >> (diff));
}
else
{
sourceToCopy = (byte)((sourceByte & sourceMask) << (diff * (-1)));
}
return (byte)(sourceToCopy | destinationToCopy);
}