PHP: Hypertext Preprocessor

Bitsel İşleçler

Bitsel işleçler, bir tamsayının içindeki belli bitleri 0 ya da 1 yaparlar.

**Bitsel İşleçler**
Örnek	İsim	Sonuç
`$a & $b`	Ve	Hem `$a` hem de `$b`'de 1 olan bitler sonuçta 1 yapılır.
`$a \| $b`	Veya	`$a` veya `$b`'de 1 olan bitler sonuçta 1 yapılır.
`$a ^ $b`	Ayrıcalıklı Veya	Hem `$a` hem de `$b`'de 0 veya 1 olan bitler sonuçta 0, diğerleri 1 yapılır.
`~ $a`	Değil	`$a`'nın 0 olan bitleri 1, 1 olanları 0 yapılır.
`$a << $b`	Sola kaydırma	`$a`'nın bitleri `$b` adım sola kaydırılır (her adım ikiyle çarpma işlemine denktir).
`$a >> $b`	Sağa kaydırma	`$a`'nın bitleri `$b` adım sağa kaydırılır (her adım ikiye bölme işlemine denktir).

PHP'de bit kaydırma bir aritmetik işlemdir. Kaydırma sonucu her iki uçtan da taşan bitler silinir. Sola kaydırmada sağdan eksilen bitler sıfırlarla doldurulur, bu arada işaret biti soldan taşarak silinir, yani sola kaydırmada terimin işareti korunmaz. Sağa kaldırmada ise işaret biti yerinden oynatılmaz, yani sağa kaydırmada terimin işareti korunur.

Bir işlemin öncelik alması gerekiyorsa yaylı ayraçlar kullanılmalıdır. Örneğin, $a & $b == true işleminde önce eşitlik sonra bitsel VE uygulanırken ($a & $b) == true işleminde ise önce bitsel VE sonra eşitlik uygulanır.

Eğer &, | ve ^ için her iki terim de dize ise terimlerdeki karakterlerin ASCII değerleri üzerinde işlem yapılır ve sonuç bir dize olur. Tüm diğer durumlarda, her iki terim tamsayıya dönüştürülür ve sonuç tamsayı olur.

~ işleci için terim bir dize ise, terimdeki karakterlerin ASCII değerleri üzerinde işlem yapılır ve sonuç bir dize olur. Aksi takdirde, terim ve sonuç tamsayı olarak ele alınır.

<< ve >> işleçleri için her iki terim ve sonuç daima tamsayı olarak ele alınır.

PHP'nin error_reporting yönergesi gerçekte neler olup bittiğini göstermek
için bitsel değerler kullanır. Sadece bilgilendirmeleri değil hataların
tümünü görmek için php.ini dosyasında ilgili yere şu yazılabilir:
E_ALL & ~E_NOTICE

Bu E_ALL için şöyle çalışır:
00000000000000000111011111111111
Keza E_NOTICE...
00000000000000000000000000001000
... ve ~ ile ters çevrilerek:
11111111111111111111111111110111
Son olarak, her iki değer üzerinde etkin bitleri bulmak için
VE (&) işlecini kullanır:
00000000000000000111011111110111

Bunu sağlamanın bir başka yolu da sadece bir değerde veya diğerinde etkin
bitleri bulmak için XOR (^) kullanmaktır:
E_ALL ^ E_NOTICE

error_reporting yönergesi bitleri etkin kılmayı göstermek için de
kullanılabilir. Sadece hataları ve kurtarılabilir göstermenin yolu:
E_ERROR | E_RECOVERABLE_ERROR

Bu işlem etkin bitleri almak için
00000000000000000000000000000001
ve
00000000000000000001000000000000
E_ERROR'ları üzerinde VEYA (|) işlecini kullanır:
00000000000000000001000000000001

Örnek 1 - Tamsayılar üzerinde bitsel işlemler

<?php
/*
 * Üstteki bölümü yoksay,
 * çıktıyı iyileştirmek için biçemlemekten başka birşey yapmıyor.
 */

$format = '(%1$2d = %1$04b) = (%2$2d = %2$04b)'
        . ' %3$s (%4$2d = %4$04b)' . "\n";

echo <<<EOH
 ---------     ---------  -- ---------
   sonuç         değer    işl   dnm
 ---------     ---------  -- ---------
EOH;


/*
 * Örnekler burada.
 */

$değerler = array(0, 1, 2, 4, 8);
$dnm = 1 + 4;

echo "\n Bitsel VE \n";
foreach ($değerler as $değer) {
    $sonuç = $değer & $dnm;
    printf($format, $sonuç, $değer, '&', $dnm);
}

echo "\n Bitsel Ayrıcalıklı VEYA \n";
foreach ($değerler as $değer) {
    $sonuç = $değer | $dnm;
    printf($format, $sonuç, $değer, '|', $dnm);
}

echo "\n Bitsel Ayrıcalıklı VEYA (XOR) \n";
foreach ($değerler as $değer) {
    $sonuç = $değer ^ $dnm;
    printf($format, $sonuç, $değer, '^', $dnm);
}
?>

Yukarıdaki örneğin çıktısı:

 ---------     ---------  -- ---------
   sonuç         değer    işl   dnm
 ---------     ---------  -- ---------
 Bitsel VE
( 0 = 0000) = ( 0 = 0000) & ( 5 = 0101)
( 1 = 0001) = ( 1 = 0001) & ( 5 = 0101)
( 0 = 0000) = ( 2 = 0010) & ( 5 = 0101)
( 4 = 0100) = ( 4 = 0100) & ( 5 = 0101)
( 0 = 0000) = ( 8 = 1000) & ( 5 = 0101)

 Bitsel Ayrıcalıklı VEYA
( 5 = 0101) = ( 0 = 0000) | ( 5 = 0101)
( 5 = 0101) = ( 1 = 0001) | ( 5 = 0101)
( 7 = 0111) = ( 2 = 0010) | ( 5 = 0101)
( 5 = 0101) = ( 4 = 0100) | ( 5 = 0101)
(13 = 1101) = ( 8 = 1000) | ( 5 = 0101)

 Bitsel Ayrıcalıklı VEYA (XOR)
( 5 = 0101) = ( 0 = 0000) ^ ( 5 = 0101)
( 4 = 0100) = ( 1 = 0001) ^ ( 5 = 0101)
( 7 = 0111) = ( 2 = 0010) ^ ( 5 = 0101)
( 1 = 0001) = ( 4 = 0100) ^ ( 5 = 0101)
(13 = 1101) = ( 8 = 1000) ^ ( 5 = 0101)

Örnek 2 - Dizgeler üzerinde bitsel işlemler

<?php
echo 12 ^ 9; // '5' çıktılar

echo "12" ^ "9"; // Gerisilme karakterini çıktılar (ASCII 8)
                 // ('1' (ascii 49)) ^ ('9' (ascii 57)) =  ASCII 8

echo "hallo" ^ "hello"; // Çıktılanan ASCII değerler #0 #4 #0 #0 #0
                        // 'a' ^ 'e' = #4

echo 2 ^ "3"; // 1 çıktılar
              // 2 ^ ((int) "3") == 1

echo "2" ^ 3; // 1 çıktılar
              // ((int) "2") ^ 3 == 1
?>

Örnek 3 - Tamsayılarda bit kaydırma

<?php
/*
 * Bunlar örnektir.
 */

echo "\n--- POZİTİF TAMSAYILARDA SAĞA BİT KAYDIRMA ---\n";

$dgr = 4;
$hane = 1;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane, 'işaret bitinin kopyası sola kaydırıldı');

$dgr = 4;
$hane = 2;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane);

$dgr = 4;
$hane = 3;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane, 'bitler sağa kaydırıldı');

$dgr = 4;
$hane = 4;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane, 'yukarıdakiyle aynı; 0\'dan sonrası kaydırılamaz');


echo "\n--- NEGATİF TAMSAYILARDA SAĞA BİT KAYDIRMA ---\n";

$dgr = -4;
$hane = 1;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane, 'işaret bitinin kopyası sola kaydırıldı');

$dgr = -4;
$hane = 2;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane, 'bitler sağa kaydırıldı');

$dgr = -4;
$hane = 3;
$snç = $dgr >> $hane;
p($snç, $dgr, '>>', $hane, 'yukarıdakiyle aynı; -1\'dan sonrası kaydırılamaz');


echo "\n--- POZİTİF TAMSAYILARDA SOLA BİT KAYDIRMA ---\n";

$dgr = 4;
$hane = 1;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane, 'sağ taraf sıfırlarla doldurulur');

$dgr = 4;
$hane = (PHP_INT_SIZE * 8) - 4;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane);

$dgr = 4;
$hane = (PHP_INT_SIZE * 8) - 3;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane, 'işaret bitleri dışa kaydırılır');

$dgr = 4;
$hane = (PHP_INT_SIZE * 8) - 2;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane, 'bitler sola kaydırıldı');


echo "\n--- NEGATİF TAMSAYILARDA SOLA BİT KAYDIRMA ---\n";

$dgr = -4;
$hane = 1;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane, 'sağ taraf sıfırlarla doldurulur');

$dgr = -4;
$hane = (PHP_INT_SIZE * 8) - 3;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane);

$dgr = -4;
$hane = (PHP_INT_SIZE * 8) - 2;
$snç = $dgr << $hane;
p($snç, $dgr, '<<', $hane, 'işaret biti dahil, bitler soldan dışa kaydırıldı');


/*
 * Bundan sonrasını yoksayın; çıktıyı biçemlemekten başka bir şey yapmıyor.
 */

function p($snç, $dgr, $op, $hane, $ilt = '') {
    $format = '%0' . (PHP_INT_SIZE * 8) . "b\n";

    printf("İfade: %d = %d %s %d\n", $snç, $dgr, $op, $hane);

    echo " Onluk:\n";
    printf("  değer=%d\n", $dgr);
    printf("  sonuç=%d\n", $snç);

    echo " İkilik:\n";
    printf('  değer=' . $format, $dgr);
    printf('  sonuç=' . $format, $snç);

    if ($ilt) {
        echo " DİKKAT: $ilt\n";
    }

    echo "\n";
}
?>

Yukarıdaki örneğin 32 bitlik makinelerdeki çıktısı:


--- POZİTİF TAMSAYILARDA SAĞA BİT KAYDIRMA ---
İfade: 2 = 4 >> 1
 Onluk:
  değer=4
  sonuç=2
 İkilik:
  değer=000000000000000000000000000100
  sonuç=000000000000000000000000000010
 DİKKAT: işaret bitinin kopyası sola kaydırıldı

İfade: 1 = 4 >> 2
 Onluk:
  değer=4
  sonuç=1
 İkilik:
  değer=000000000000000000000000000100
  sonuç=000000000000000000000000000001

İfade: 0 = 4 >> 3
 Onluk:
  değer=4
  sonuç=0
 İkilik:
  değer=000000000000000000000000000100
  sonuç=000000000000000000000000000000
 DİKKAT: bitler sağa kaydırıldı

İfade: 0 = 4 >> 4
 Onluk:
  değer=4
  sonuç=0
 İkilik:
  değer=000000000000000000000000000100
  sonuç=000000000000000000000000000000
 DİKKAT: yukarıdakiyle aynı; 0'dan sonrası kaydırılamaz


--- NEGATİF TAMSAYILARDA SAĞA BİT KAYDIRMA ---
İfade: -2 = -4 >> 1
 Onluk:
  değer=-4
  sonuç=-2
 İkilik:
  değer=111111111111111111111111111100
  sonuç=111111111111111111111111111110
 DİKKAT: işaret bitinin kopyası sola kaydırıldı

İfade: -1 = -4 >> 2
 Onluk:
  değer=-4
  sonuç=-1
 İkilik:
  değer=111111111111111111111111111100
  sonuç=111111111111111111111111111111
 DİKKAT: bitler sağa kaydırıldı

İfade: -1 = -4 >> 3
 Onluk:
  değer=-4
  sonuç=-1
 İkilik:
  değer=111111111111111111111111111100
  sonuç=111111111111111111111111111111
 DİKKAT: yukarıdakiyle aynı; -1'dan sonrası kaydırılamaz


--- POZİTİF TAMSAYILARDA SOLA BİT KAYDIRMA ---
İfade: 8 = 4 << 1
 Onluk:
  değer=4
  sonuç=8
 İkilik:
  değer=000000000000000000000000000100
  sonuç=000000000000000000000000001000
 DİKKAT: sağ taraf sıfırlarla doldurulur

İfade: 4611686018427387904 = 4 << 60
 Onluk:
  değer=4
  sonuç=4611686018427387904
 İkilik:
  değer=000000000000000000000000000100
  sonuç=010000000000000000000000000000

İfade: -9223372036854775808 = 4 << 61
 Onluk:
  değer=4
  sonuç=-9223372036854775808
 İkilik:
  değer=000000000000000000000000000100
  sonuç=100000000000000000000000000000
 DİKKAT: işaret bitleri dışa kaydırılır

İfade: 0 = 4 << 62
 Onluk:
  değer=4
  sonuç=0
 İkilik:
  değer=000000000000000000000000000100
  sonuç=000000000000000000000000000000
 DİKKAT: bitler sola kaydırıldı


--- NEGATİF TAMSAYILARDA SOLA BİT KAYDIRMA ---
İfade: -8 = -4 << 1
 Onluk:
  değer=-4
  sonuç=-8
 İkilik:
  değer=111111111111111111111111111100
  sonuç=111111111111111111111111111000
 DİKKAT: sağ taraf sıfırlarla doldurulur

İfade: -9223372036854775808 = -4 << 61
 Onluk:
  değer=-4
  sonuç=-9223372036854775808
 İkilik:
  değer=111111111111111111111111111100
  sonuç=100000000000000000000000000000

İfade: 0 = -4 << 62
 Onluk:
  değer=-4
  sonuç=0
 İkilik:
  değer=111111111111111111111111111100
  sonuç=000000000000000000000000000000
 DİKKAT: işaret biti dahil, bitler soldan dışa kaydırıldı

Yukarıdaki örneğin 64 bitlik makinelerdeki çıktısı:


--- POZİTİF TAMSAYILARDA SAĞA BİT KAYDIRMA ---
İfade: 2 = 4 >> 1
 Onluk:
  değer=4
  sonuç=2
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0000000000000000000000000000000000000000000000000000000000000010
 DİKKAT: işaret bitinin kopyası sola kaydırıldı

İfade: 1 = 4 >> 2
 Onluk:
  değer=4
  sonuç=1
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0000000000000000000000000000000000000000000000000000000000000001

İfade: 0 = 4 >> 3
 Onluk:
  değer=4
  sonuç=0
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0000000000000000000000000000000000000000000000000000000000000000
 DİKKAT: bitler sağa kaydırıldı

İfade: 0 = 4 >> 4
 Onluk:
  değer=4
  sonuç=0
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0000000000000000000000000000000000000000000000000000000000000000
 DİKKAT: yukarıdakiyle aynı; 0'dan sonrası kaydırılamaz


--- NEGATİF TAMSAYILARDA SAĞA BİT KAYDIRMA ---
İfade: -2 = -4 >> 1
 Onluk:
  değer=-4
  sonuç=-2
 İkilik:
  değer=1111111111111111111111111111111111111111111111111111111111111100
  sonuç=1111111111111111111111111111111111111111111111111111111111111110
 DİKKAT: işaret bitinin kopyası sola kaydırıldı

İfade: -1 = -4 >> 2
 Onluk:
  değer=-4
  sonuç=-1
 İkilik:
  değer=1111111111111111111111111111111111111111111111111111111111111100
  sonuç=1111111111111111111111111111111111111111111111111111111111111111
 DİKKAT: bitler sağa kaydırıldı

İfade: -1 = -4 >> 3
 Onluk:
  değer=-4
  sonuç=-1
 İkilik:
  değer=1111111111111111111111111111111111111111111111111111111111111100
  sonuç=1111111111111111111111111111111111111111111111111111111111111111
 DİKKAT: yukarıdakiyle aynı; -1'dan sonrası kaydırılamaz


--- POZİTİF TAMSAYILARDA SOLA BİT KAYDIRMA ---
İfade: 8 = 4 << 1
 Onluk:
  değer=4
  sonuç=8
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0000000000000000000000000000000000000000000000000000000000001000
 DİKKAT: sağ taraf sıfırlarla doldurulur

İfade: 4611686018427387904 = 4 << 60
 Onluk:
  değer=4
  sonuç=4611686018427387904
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0100000000000000000000000000000000000000000000000000000000000000

İfade: -9223372036854775808 = 4 << 61
 Onluk:
  değer=4
  sonuç=-9223372036854775808
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=1000000000000000000000000000000000000000000000000000000000000000
 DİKKAT: işaret bitleri dışa kaydırılır

İfade: 0 = 4 << 62
 Onluk:
  değer=4
  sonuç=0
 İkilik:
  değer=0000000000000000000000000000000000000000000000000000000000000100
  sonuç=0000000000000000000000000000000000000000000000000000000000000000
 DİKKAT: bitler sola kaydırıldı


--- NEGATİF TAMSAYILARDA SOLA BİT KAYDIRMA ---
İfade: -8 = -4 << 1
 Onluk:
  değer=-4
  sonuç=-8
 İkilik:
  değer=1111111111111111111111111111111111111111111111111111111111111100
  sonuç=1111111111111111111111111111111111111111111111111111111111111000
 DİKKAT: sağ taraf sıfırlarla doldurulur

İfade: -9223372036854775808 = -4 << 61
 Onluk:
  değer=-4
  sonuç=-9223372036854775808
 İkilik:
  değer=1111111111111111111111111111111111111111111111111111111111111100
  sonuç=1000000000000000000000000000000000000000000000000000000000000000

İfade: 0 = -4 << 62
 Onluk:
  değer=-4
  sonuç=0
 İkilik:
  değer=1111111111111111111111111111111111111111111111111111111111111100
  sonuç=0000000000000000000000000000000000000000000000000000000000000000
 DİKKAT: işaret biti dahil, bitler soldan dışa kaydırıldı

Uyarı

PHP_INT_MAX'ın ötesindeki sayılar üzerinde bitsel işlemler için gmp eklentisindeki işlevler kullanılmalıdır.

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User Contributed Notes 27 notes

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117

wbcarts at juno dot com ¶

12 years ago

BITWISE FLAGS for Custom PHP Objects

Sometimes I need a custom PHP Object that holds several boolean TRUE or FALSE values. I could easily include a variable for each of them, but as always, code has a way to get unweildy pretty fast. A more intelligent approach always seems to be the answer, even if it seems to be overkill at first.

I start with an abstract base class which will hold a single integer variable called $flags. This simple integer can hold 32 TRUE or FALSE boolean values. Another thing to consider is to just set certain BIT values without disturbing any of the other BITS -- so included in the class definition is the setFlag($flag, $value) function, which will set only the chosen bit. Here's the abstract base class definition: 

<?php

# BitwiseFlag.php

abstract class BitwiseFlag
{
  protected $flags;

  /*
   * Note: these functions are protected to prevent outside code
   * from falsely setting BITS. See how the extending class 'User'
   * handles this.
   *
   */
  protected function isFlagSet($flag)
  {
    return (($this->flags & $flag) == $flag);
  }

  protected function setFlag($flag, $value)
  {
    if($value)
    {
      $this->flags |= $flag;
    }
    else
    {
      $this->flags &= ~$flag;
    }
  }
}

?>

The class above is abstract and cannot be instantiated, so an extension is required. Below is a simple extension called User -- which is severely truncated for clarity. Notice I am defining const variables AND methods to use them.

<?php

# User.php

require('BitwiseFlag.php');

class User extends BitwiseFlag
{
  const FLAG_REGISTERED = 1; // BIT #1 of $flags has the value 1
  const FLAG_ACTIVE = 2;     // BIT #2 of $flags has the value 2
  const FLAG_MEMBER = 4;     // BIT #3 of $flags has the value 4
  const FLAG_ADMIN = 8;      // BIT #4 of $flags has the value 8

  public function isRegistered(){
    return $this->isFlagSet(self::FLAG_REGISTERED);
  }

  public function isActive(){
    return $this->isFlagSet(self::FLAG_ACTIVE);
  }

  public function isMember(){
    return $this->isFlagSet(self::FLAG_MEMBER);
  }

  public function isAdmin(){
    return $this->isFlagSet(self::FLAG_ADMIN);
  }

  public function setRegistered($value){
    $this->setFlag(self::FLAG_REGISTERED, $value);
  }

  public function setActive($value){
    $this->setFlag(self::FLAG_ACTIVE, $value);
  }

  public function setMember($value){
    $this->setFlag(self::FLAG_MEMBER, $value);
  }

  public function setAdmin($value){
    $this->setFlag(self::FLAG_ADMIN, $value);
  }

  public function __toString(){
    return 'User [' .
      ($this->isRegistered() ? 'REGISTERED' : '') .
      ($this->isActive() ? ' ACTIVE' : '') .
      ($this->isMember() ? ' MEMBER' : '') .
      ($this->isAdmin() ? ' ADMIN' : '') .
    ']';
  }
}

?>

This seems like a lot of work, but we have addressed many issues, for example, using and maintaining the code is easy, and the getting and setting of flag values make sense. With the User class, you can now see how easy and intuitive bitwise flag operations become.

<?php

require('User.php')

$user = new User();
$user->setRegistered(true);
$user->setActive(true);
$user->setMember(true);
$user->setAdmin(true);

echo $user;  // outputs: User [REGISTERED ACTIVE MEMBER ADMIN]

?>

down

grayda dot NOSPAM at DONTSPAM dot solidinc dot org ¶

15 years ago

Initially, I found bitmasking to be a confusing concept and found no use for it. So I've whipped up this code snippet in case anyone else is confused:

<?php

    // The various details a vehicle can have
    $hasFourWheels = 1;
    $hasTwoWheels  = 2;
    $hasDoors      = 4;
    $hasRedColour  = 8;

    $bike          = $hasTwoWheels;
    $golfBuggy     = $hasFourWheels;
    $ford          = $hasFourWheels | $hasDoors;
    $ferrari       = $hasFourWheels | $hasDoors | $hasRedColour;

    $isBike        = $hasFourWheels & $bike; # False, because $bike doens't have four wheels
    $isGolfBuggy   = $hasFourWheels & $golfBuggy; # True, because $golfBuggy has four wheels
    $isFord        = $hasFourWheels & $ford; # True, because $ford $hasFourWheels

?>

And you can apply this to a lot of things, for example, security:

<?php

    // Security permissions:
    $writePost = 1;
    $readPost = 2;
    $deletePost = 4;
    $addUser = 8;
    $deleteUser = 16;
    
    // User groups:
    $administrator = $writePost | $readPosts | $deletePosts | $addUser | $deleteUser;
    $moderator = $readPost | $deletePost | $deleteUser;
    $writer = $writePost | $readPost;
    $guest = $readPost;

    // function to check for permission
    function checkPermission($user, $permission) {
        if($user & $permission) {
            return true;
        } else {
            return false;
        }
    }

    // Now we apply all of this!
    if(checkPermission($administrator, $deleteUser)) {
        deleteUser("Some User"); # This is executed because $administrator can $deleteUser
    }

?>

Once you get your head around it, it's VERY useful! Just remember to raise each value by the power of two to avoid problems

down

S?b. ¶

19 years ago

A bitwise operators practical case :

<?php
    // We want to know the red, green and blue values of this color :
    $color = 0xFEA946 ;

    $red = $color >> 16 ;
    $green = ($color & 0x00FF00) >> 8 ;
    $blue = $color & 0x0000FF ;

    printf('Red : %X (%d), Green : %X (%d), Blue : %X (%d)',
        $red, $red, $green, $green, $blue, $blue) ;

    // Will display...
    // Red : FE (254), Green : A9 (169), Blue : 46 (70)
?>

down

frankemeks77 at yahoo dot com ¶

12 years ago

Just learning Bitwise Shift Operators.



The easiest way to resolve a bitwise  shift operators is my multiply or dividing each step by two for left shift or right shift respectively



Example:



LEFT SHIFT

<?php echo 8 << 3; //64 ?>



//same as

<?php echo 8 * 2 * 2 * 2; ?>



RIGHT SHIFT

<?php echo 8 >> 3; //1 ?>



//same as

<?php echo ((8/2)/2)/2; //1 ?>



//Solving on a paper 8/2 = 4/2 = 2/2 = 1

down

Silver ¶

15 years ago

Regarding what Bob said about flags, I'd like to point out there's a 100% safe way of defining flags, which is using hexadecimal notation for integers:

<?php
define("f0", 0x1); // 2^0
define("f1", 0x2); // 2^1
define("f2", 0x4); // 2^2
define("f3", 0x8); // 2^3
define("f4", 0x10); // 2^4
define("f5", 0x20); // 2^5
// ...
define("f20", 0x1000000); // 2^20
define("f21", 0x2000000); // 2^21
define("f22", 0x4000000); // 2^22
define("f23", 0x8000000); // 2^23
define("f24", 0x10000000); // 2^24
// ... up to 2^31
?>

I always avoid using decimal notation when I have a large amount of different flags, because it's very easy to misspell numbers like 2^20 (1048576).

down

zlel grxnslxves13 at hotmail dot com~=s/x/ee/g ¶

19 years ago

I refer to Eric Swanson's post on Perl VS PHP's implementation of xor. 

Actually, this is not an issue with the implementation of XOR,  but a lot more to do with the lose-typing policy that PHP adopts. 

Freely switching between int and float is good for most cases, but problems happen when your value is near the word size of your machine. Which is to say, 32-bit machines will encounter problems with values that hover around 0x80000000 - primarily because PHP does not support unsigned integers.

using bindec/decbin would address this issue as a work-around to do unsigned-int xor, but here's the real picture (i'm not claiming that this code will perform better, but this would be a better pedagogical code):

<?php

function unsigned_xor32 ($a, $b) 
{
        $a1 = $a & 0x7FFF0000;
        $a2 = $a & 0x0000FFFF;
        $a3 = $a & 0x80000000;
        $b1 = $b & 0x7FFF0000;
        $b2 = $b & 0x0000FFFF;
        $b3 = $b & 0x80000000;

        $c = ($a3 != $b3) ? 0x80000000 : 0;

        return (($a1 ^ $b1) |($a2 ^ $b2)) + $c;
}

$x = 3851235679;
$y = 43814;
echo "<br>This is the value we want";
echo "<br>3851262585";

echo "<br>The result of a native xor operation on integer values is treated as a signed integer";
echo "<br>".($x ^ $y);

echo "<br>We therefore perform the MSB separately";
echo "<br>".unsigned_xor32($x, $y);

?>

This is really foundation stuff, but for those of you who missed this in college, there seems to be something on 2's complement here: 

http://www.evergreen.edu/biophysics/technotes/program/2s_comp.htm

down

m0sh at hotmail dot com ¶

16 years ago

@greenone - nice function, thanks. I've adapted it for key usage:

<?php
function bitxor($str, $key) {
    $xorWidth = PHP_INT_SIZE*8;
    // split
    $o1 = str_split($str, $xorWidth);
    $o2 = str_split(str_pad('', strlen($str), $key), $xorWidth);
    $res = '';
    $runs = count($o1);
    for($i=0;$i<$runs;$i++)
        $res .= decbin(bindec($o1[$i]) ^ bindec($o2[$i]));       
    return $res;
}
?>

down

zewt at hotmail dot com ¶

17 years ago

if you use bitwise you MUST make sure your variables are integers, otherwise you can get incorrect results.

I recommend ALWAYS

(int)$var & (int)$var2

This will save you many headaches when troubleshooting a completely illogical result.

down

zooly at globmi dot com ¶

15 years ago

Here is an example for bitwise leftrotate and rightrotate.

Note that this function works only with decimal numbers - other types can be converted with pack().

<?php

function rotate ( $decimal, $bits) {

  $binary = decbin($decimal);

  return (
    bindec(substr($binary, $bits).substr($binary, 0, $bits))
  );

}

// Rotate 124 (1111100) to the left with 1 bits

echo rotate(124, 1);

// = 121 (1111001)

// Rotate 124 (1111100) to the right with 3 bits

echo rotate(124, -3);

// = 79 (1001111)

?>

down

vivekanand dot pathak25 at gmail dot com ¶

11 years ago

$a =     9;
$b =     10;
echo $a & $b;

place value   128  64  32  16   8  4   2   1
$a                     0      0    0     0    1  0   0   1   =9
$b                     0      0    0     0    1   0  1   0   =10

result   8  

 only bit they share together is the 8 bit. So 8 gets returned.

  $a =     36;
$b =     103;
echo $a & $b;

place value   128  64  32  16   8    4   2   1
$a                     0      0    1     0    0    1   0   0   =36
$b                     0      1    1     0    0    1   1   1   =103

result  32+4 = 36
the only bits these two share together are the bits 32 and 4 which when added together return 36.

$a =     9;
$b =     10;
echo $a | $b;

place value   128  64  32  16   8  4   2   1
$a                     0      0    0     0    1  0   0   1   =9
$b                     0      0    0     0    1   0  1   0   =10

result 8+2+1 = 11
 3 bits set, in the 8, 2, and 1 column.add those up 8+2+1 and you get 11

$a =     9;
$b =     10;
echo $a ^ $b;

place value   128  64  32  16   8  4   2   1
$a                     0      0    0     0    1  0   0   1   =9
$b                     0      0    0     0    1   0  1   0   =10

result  2+1 = 3
the 2 bit and the 1 bit that they each have set but don't share. Soooo 2+1 = 3

down

ASchmidt at Anamera dot net ¶

5 years ago

Setting, unsetting and testing single and multiple bits in a bitmask:

<?php
    const    FLAG_A    =    0b0001,
            FLAG_B    =    0b0010,
            FLAG_C    =    0b0100,
            FLAG_D    =    0b1000;
            
    const    COMBO_BC = FLAG_B | FLAG_C;

    $bitmask = 0b000;
    
    // Setting individual flags.
    $bitmask |=    FLAG_B;        // Sets FLAG_B (=2)
    $bitmask |=    FLAG_C;        // also sets FLAG_C (=4)
    
    // Testing single or multiple flags.
    echo (bool)( $bitmask & FLAG_B );                            // True, B is set.
    
    echo (bool)( $bitmask & (FLAG_A | FLAG_B) );                // True, A or B is set.
    
    echo (bool)( $bitmask & FLAG_B and $bitmask & FLAG_C );        // True, B and C are set.
    echo (bool)( ( $bitmask & (FLAG_B | FLAG_C) ) ^ (FLAG_B | FLAG_C) );    // False if B and C are set.
    echo (bool)( ( $bitmask & COMBO_BC ) ^ COMBO_BC );            // False if B and C are set.
    
    echo (bool)( $bitmask & FLAG_C and $bitmask & FLAG_D );        // False, C and D are NOT BOTH set.
    echo (bool)( ( $bitmask & (FLAG_C | FLAG_D) ) ^ (FLAG_C | FLAG_D) );    // True, if C and D are NOT BOTH set.
    
    // Resetting single flag.
    $bitmask &= $bitmask ^ FLAG_B;    // Unsets B
    $bitmask &= $bitmask ^ FLAG_A;    // A remains unset.
    var_dump( $bitmask );            // Only C still set (=4)
    
    // Resetting multiple flags.
    $bitmask &= $bitmask ^ ( FLAG_C | FLAG_D );    // Unsets C and/or D
    var_dump( $bitmask );            // No flags set (=0)

down

josh at joshstrike dot com ¶

13 years ago

More referencing this for myself than anything... if you need to iterate through every possible binary combination where $n number of flags are set to 1 in a mask of $bits length:



<?php

echo masksOf(3,10);



function masksOf($n,$bits) {

    $u = pow(2,$bits)-1; //start value, full flags on.

    $masks = array();

    while ($u>0) {

        $z = numflags($u);

        if ($z==$n) array_push($masks,$u);

        $u--;

    }

    return ($masks);    

}



function numflags($n) {

    $k = 0;

    while ($n) {

        $k += $n & 1;

        $n = $n >> 1;

    }

    return ($k);



//    alternately: 

//    $u = 0;

//    for ($k=1;$k<=$n;$k*=2) {

//        $u+=($n&$k?1:0);

//    }

//    return ($u);

}

?>

down

amckenzie4 at gmail dot com ¶

14 years ago

If, like me, you've never thought about how PHP deals with binary, the output of the bitwise NOT may confuse you.  For instance, this:

$bin = 2;
$notbin = ~$bin;

echo "Bin: " . decbin($bin) . "  !bin:  " . decbin($notbin) . "\n";

returns this:

Bin: 10  !bin:  1111111111111111111111111111111111111111111111111111111111111101

The reason is that all binary numbers are treated as 32 bits, even if you've manually entered less.  In order to get the result I expected (01), it was necessary to AND the result with the number of bits I wanted:  in this case, 2 (the number 3, in decimal).  Be aware that all return values will have zeros removed from the left until they reach a bit that is set to 1.  Continuing the above example, the following:

$notbin_2 = ~$bin & '3';
echo "!bin & 3:  " . decbin($notbin_2) . "\n";

returns this:

!bin & 3:  1

Note that the actual value was a string of 31 zeros followed by a 1, but the zeros were not shown.  This is probably a good thing.

Furthermore, the NOT operator uses two's complement, which means the number you get may be even stranger than you expect:  using two's complement means that ~2 == -3.  There are plenty of good explanations of two's complement online, so I won't go into that question here.

If what you want is just to reverse a string of bits without any interpretation, you can use a function like this:

function bitnot($bin)
 {
   $not = "";
   for ($i = 0; $i < strlen($bin); $i++)
   {
      if($bin[$i] == 0) { $not .= '1'; }
      if($bin[$i] == 1) { $not .= '0'; }
   }
   return $not;
 }

It takes a binary string of any length, reverses the bits, and returns the new string.  You can then treat it as a binary number, use bindec() to turn it into a decimal, or whatever you want.

I hope this helps someone as much as it would have helped me a week ago!

down

Tbrendstrup ¶

19 years ago

note that the shift operators are arithmetic, not logic like in C. You may get unexpected results with negative numbers, see http://en.wikipedia.org/wiki/Bitwise_operation

here's a function to do logic right shifts.

<?php

function lshiftright($var,$amt)
{
    $mask = 0x40000000;
    if($var < 0)
    {
        $var &= 0x7FFFFFFF;
        $mask = $mask >> ($amt-1);
        return ($var >> $amt) | $mask;
    }
    return $var >> $amt;
}

$val = -10;

printf("arithmetic shift on a negative integer<br>%1\$032b<br>%2\$032b<br>%1\$0d<br>%2\$0d<br>",$val, $val >> 1 );

printf("logic shift on a negative integer<br>%1\$032b<br>%2\$032b<br>%1\$0d<br>%2\$0d<br>",$val, lshiftright($val, 1));

printf("logic shift on a positive integer<br>%1\$032b<br>%2\$032b<br>%1\$0d<br>%2\$0d<br>",-$val, lshiftright(-$val, 1));
?>

gives the output:

arithmetic shift on a negative integer
11111111111111111111111111110110
11111111111111111111111111111011
-10
-5

logic shift on a negative integer
11111111111111111111111111110110
01111111111111111111111111111011
-10
2147483643

logic shift on a positive integer
00000000000000000000000000001010
00000000000000000000000000000101
10
5

down

spencer-p-moy at example dot com ¶

13 years ago

The NOT or complement operator ( ~ ) and negative binary numbers can be confusing.

~2 = -3  because you use the formula  ~x = -x - 1  The bitwise complement of a decimal number is the negation of the number minus 1.

NOTE: just using 4 bits here for the examples below but in reality PHP uses 32 bits.

Converting a negative decimal number (ie: -3) into binary takes 3 steps:
1) convert the positive version of the decimal number into binary (ie: 3 = 0011)
2) flips the bits (ie: 0011 becomes 1100)
3) add 1 (ie: 1100  + 0001 = 1101)

You might be wondering how does 1101 = -3. Well PHP uses the method "2's complement" to render negative binary numbers. If the left most bit is a 1 then the binary number is negative and you flip the bits and add 1. If it is 0 then it is positive and you don't have to do anything. So 0010 would be a positive 2. If it is 1101, it is negative and you flip the bits to get 0010. Add 1 and you get 0011 which equals -3.

down

aba at example dot com ¶

13 years ago

It is true that if both the left-hand and right-hand parameters are strings, the bitwise operator will operate on the characters' ASCII values. However, a complement is necessary to complete this sentence.
It is not irrelevant to point out that the decimal character's ASCII value have different binary values.

<?php
if (('18' & '32') == '10') {
    echo ord('18'); //return decimal value 49, which have binary value 110001
    echo ord('32'); //return decimal value 51, which have binary value 110011
    echo ord('10'); //return decimal value 49, which have binary value 110001
    //Therefore 110001 & 110011 = 110001
}
?>

down

icy at digitalitcc dot com ¶

19 years ago

Say... you really want to have say... more than 31 bits available to you in your happy bitmask. And you don't want to use floats. So, one solution would to have an array of bitmasks, that are accessed through some kind of interface.

Here is my solution for this: A class to store an array of integers being the bitmasks. It can hold up to 66571993087 bits, and frees up unused bitmasks when there are no bits being stored in them.

<?php
/*
    Infinite* bits and bit handling in general.
    
    *Not infinite, sorry.
    
    Perceivably, the only limit to the bitmask class in storing bits would be
    the maximum limit of the index number, on 32 bit integer systems 2^31 - 1,
    so 2^31 * 31 - 1 = 66571993087 bits, assuming floats are 64 bit or something.
    I'm sure that's enough enough bits for anything.. I hope :D.
*/

DEFINE('INTEGER_LENGTH',31); // Stupid signed bit.

class bitmask
{
    protected $bitmask = array();
    
    public function set( $bit ) // Set some bit
    {
        $key = (int) ($bit / INTEGER_LENGTH);
        $bit = (int) fmod($bit,INTEGER_LENGTH);
        $this->bitmask[$key] |= 1 << $bit;
    }
    
    public function remove( $bit ) // Remove some bit
    {
        $key = (int) ($bit / INTEGER_LENGTH);
        $bit = (int) fmod($bit,INTEGER_LENGTH);
        $this->bitmask[$key] &= ~ (1 << $bit);
        if(!$this->bitmask[$key])
            unset($this->bitmask[$key]);
    }
    
    public function toggle( $bit ) // Toggle some bit
    {
        $key = (int) ($bit / INTEGER_LENGTH);
        $bit = (int) fmod($bit,INTEGER_LENGTH);
        $this->bitmask[$key] ^= 1 << $bit;
        if(!$this->bitmask[$key])
            unset($this->bitmask[$key]);
    }
    
    public function read( $bit ) // Read some bit
    {
        $key = (int) ($bit / INTEGER_LENGTH);
        $bit = (int) fmod($bit,INTEGER_LENGTH);
        return $this->bitmask[$key] & (1 << $bit);
    }

    public function stringin($string) // Read a string of bits that can be up to the maximum amount of bits long.
    {
        $this->bitmask = array();
        $array = str_split( strrev($string), INTEGER_LENGTH );
        foreach( $array as $key => $value )
        {
            if($value = bindec(strrev($value)))
                $this->bitmask[$key] = $value;
        }
    }

    public function stringout() // Print out a string of your nice little bits
    {
        $string = "";

        $keys = array_keys($this->bitmask);
        sort($keys, SORT_NUMERIC);

        for($i = array_pop($keys);$i >= 0;$i--)
        {
            if($this->bitmask[$i])
                $string .= sprintf("%0" . INTEGER_LENGTH . "b",$this->bitmask[$i]);
        }
        return $string;
    }
    
    public function clear() // Purge!
    {
        $this->bitmask = array();
    }
    
    public function debug() // See what's going on in your bitmask array
    {
        var_dump($this->bitmask);
    }
}
?>

It treats a positive integer input as a bit, so you don't have to deal with the powers of 2 yourself.

<?php
$bitmask = new bitmask();

$bitmask->set(8979879); // Whatever

$bitmask->set(888);

if($bitmask->read(888))
    print 'Happy!\n';

$bitmask->toggle(39393); // Yadda yadda

$bitmask->remove(888);

$bitmask->debug();

$bitmask->stringin("100101000101001000101010010101010
00000001000001");

print $bitmask->stringout() . "\n";

$bitmask->debug();

$bitmask->clear();

$bitmask->debug();
?>

Would produce:

Happy!

array(2) {
  [289673]=>
  int(65536)
  [1270]=>
  int(8388608)
}

0000000000000001001010001010010001010100101010100
0000001000001

array(2) {
  [0]=>
  int(355106881)
  [1]=>
  int(37970)
}

array(0) {
}

down

ivoras at gmail dot com ¶

13 years ago

As an additional curiosity, for some reason the result of the operation ("18" & "32") is "10". In other words, try avoiding using the binary operators on strings :)

down

Eric Swanson ¶

19 years ago

Perl vs. PHP implementation of the ^ operator:

After attempting to translate a Perl module into PHP, I realized that Perl's implementation of the ^ operator is different than the PHP implementation.  By default, Perl treats the variables as floats and PHP as integers.  I was able to verify the PHP use of the operator by stating "use integer;" within the Perl module, which output the exact same result as PHP was using.

The logical decision would be to cast every variable as (float) when using the ^ operator in PHP.  However, this will not yield the same results.  After about a half hour of banging my head against the wall, I discovered a gem and wrote a function using the binary-decimal conversions in PHP.

/*
not having much experience with bitwise operations, I cannot tell you that this is the BEST solution, but it certainly is a solution that finally works and always returns the EXACT same result Perl provides.
*/
function binxor($a, $b) {
    return bindec(decbin((float)$a ^ (float)$b));
}

//normal PHP code will not yeild the same result as Perl
$result = 3851235679 ^ 43814; //= -443704711

//to get the same result as Perl
$result = binxor(3851235679, 43814); //= 3851262585
//YIPPEE!!!

//to see the differences, try the following
$a = 3851235679 XOR 43814;
$b = 3851235679 ^ 43814; //integer result
$c = (float)3851235679 ^ (float)43814; //same as $b
$d = binxor(3851235679, 43814); //same as Perl!!

echo("A: $a<br />");
echo("B: $b<br />");
echo("C: $c<br />");
echo("D: $d<br />");

down

forlamp at msn dot com ¶

17 years ago

two's complement logical operation for 32-bit.

$x must be (int) when passing it to this function to work properly.

function comp2($x)      // 32bit bitwise complement
{
    $mask = 0x80000000;

    if ($x < 0)
    {
        $x &= 0x7FFFFFFF;
        $x = ~$x;

        return $x ^ $mask;
    }
    else
    {
        $x = $x ^ 0x7FFFFFFF;

        return $x | $mask;
    }
}

down

cw3theophilus at gmail dot com ¶

15 years ago

For those who are looking for a circular bit shift function in PHP (especially useful for cryptographic functions) that works with negtive values, here is a little function I wrote:

(Note: It took me almost a whole day to get this to work with negative $num values (I couldn't figure out why it sometimes worked and other times didn't), because PHP only has an arithmatic and not a logical bitwise right shift like I am used to. I.e. 0x80000001>>16 will ouputs (in binary) "1111 1111 1111 1111 1000 0000 0000 0000" instead of "0000 0000 0000 0000 1000 0000 0000 0000" like you would expect. To fix this you have to apply the mask (by bitwise &) equal to 0x7FFFFFFF right shifted one less than the offset you are shifting by.)

<?php
function circular_shift($num,$offset) { //Do a nondestructive circular bitwise shift, if offset positive shift left, if negative shift right
    $num=(int)$num;
    $mask=0x7fffffff; //Mask to cater for the fact that PHP only does arithmatic right shifts and not logical i.e. PHP doesn't give expected output when right shifting negative values
    if ($offset>0) {
        $num=($num<<$offset%32) | (($num>>(32-$offset%32)) & ($mask>>(31-$offset%32)));
    }
    elseif ($offset<0){
        $offset=abs($offset);
        $num=(($num>>$offset%32) & ($mask>>(-1+$offset%32))) | ($num<<(32-$offset%32));
    }
    return $num; 
}
?>

down

sag at ich dot net ¶

11 years ago

me reimplement for bitwise NOT (~)

    protected function flipBin($number) {
        $bin = str_pad(base_convert($number, 10, 2), 32, 0, STR_PAD_LEFT);
        for ($i = 0; $i < 32; $i++) {
            switch ($bin{$i}) {
                case '0' :
                    $bin{$i} = '1';
                    break;
                case '1' :
                    $bin{$i} = '0';
                    break;
            }
        }
        return bindec($bin);
    }

the benefit is, it works with numbers greater MAX_INT

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Adam ¶

14 years ago

Be careful of order of operations.

for example, you may want to check if the second bit is set:

<?php
if ($x & 2 == 2) {
    /* code */
}
?>

is different than

<?php
if (($x & 2) == 2) {
    /* code */
}
?>

and the latter of the two should be used.

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Anonymous ¶

13 years ago

To make very clear why ("18" & "32") is "10".
1) they they are both strings ,
2) "&" operator works on strings by taking each !Character! from each string and make a bit wise & between them and add this value to the resulting string

So:
"18" is made up of two characters: 0x31, 0x38
"32" is made up of two characters: 0x33, 0x32
----RESULT-----
0x31 & 0x33 = 0x31 => "1"
0x38 & 0x32 = 0x30 => "0"

and the result is "10" which is 100% correct.

down

-1

erich at seachawaii dot com ¶

12 years ago

Just a note regarding negative shift values, as the documentation states each shift is an integer multiply or divide (left or right respectively) by 2.  That means a negative shift value (the right hand operand) effects the sign of the shift and NOT the direction of the shift as I would have expected.  
FE. 0xff >> -2 results in 0x0 
and 0xff << -2 result in 0xFFFFFFFFC0000000 (dependant on PHP_INT_MAX)

down

-1

Core Xii ¶

14 years ago

Be very careful when XOR-ing strings! If one of the values is empty (0, '', null) the result will also be empty!

<?php
var_dump(1234 ^ 0); // int(1234)
var_dump(1234 ^ ''); // int(1234)
var_dump(1234 ^ null); // int(1234)
var_dump('hello world' ^ 0); // int(0)
var_dump('hello world' ^ ''); // string(0) ""
var_dump('hello world' ^ null); // int(0)
?>

This seems rather inconsistent behavior. An integer XOR'd with zero results the original integer. But a string XOR'd with an empty value results an empty value!

My password hashing function was always returning the same hash... Because I was XOR-ing it with a salt that was sometimes empty!

down

-2

Bob ¶

15 years ago

Here is an easy way to use bitwise operation for 'flag' functionality.
By this I mean managing a set of options which can either be ON or OFF, where zero or more of these options may be set and each option may only be set once. (If you are familiar with MySQL, think 'set' datatype).
Note: to older programmers, this will be obvious.

Here is the code:
<?php
function set_bitflag(/*variable-length args*/)
{
    $val = 0;
    foreach(func_get_args() as $flag) $val = $val | $flag;
    return $val;
}
function is_bitflag_set($val, $flag)
{
    return (($val & $flag) === $flag);
}
// Define your flags
define('MYFLAGONE', 1); // 0001
define('MYFLAGTWO', 2); // 0010
define('MYFLAGTHREE', 4); // 0100
define('MYFLAGFOUR', 8); // 1000
?>

I should point out: your flags are stored in a single integer. You can store loads of flags in a single integer.

To use my functions, say you wanted to set MYFLAGONE and MYFLAGTHREE, you would use:
<?php
$myflags = set_bitflags(MYFLAGONE, MYFLAGTHREE);
?>
Note: you can pass set_bitflags() as many flags to set as you want.

When you want to test later if a certain flag is set, use e.g.:
<?php
if(is_bitflag_set($myflags, MYFLAGTWO))
{
    echo "MYFLAGTWO is set!";
}
?>

The only tricky part is defining your flags. Here is the process:
1.  Write a list of your flags
2.  Count them
3.  Define the last flag in your list as 1 times 2 to the power of <count> minus one. ( I.E. 1*2^(<count>-1) )
3. Working backwards through your list, from the last to the first, define each one as half of the previous one. You should reach 1 when you get to the first

If you want to understand binary numbers, bits and bitwise operation better, the wikipedia page explains it well - http://en.wikipedia.org/wiki/Bitwise_operation.

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