Using Binary to store a selection as integer

Question

I know this is possible, I just simply don't know what its called, and Google hasn't been much help.

Lets say you have 4 options to choose from, A, B, C and D. If a user selects A and C, you can simply save the selection as 5 which = 0101, or 8 if a user selects D (1000).

My question is, how would you convert 5 back into A=1, B=0, C=1, D=0 after it was saved?

I'm trying to save film Age Restrictions, and thought this might be the best way to do it.

Answer 1

I believe the term is BCD (Binary Coded Decimal).

Here is how you could implement it in your situation:

1. Create 4 Variables (or constants) representing the 4 possible choices, and set their values like this:
   

   $A = 1;
   $B = 2;
   $C = 4;
   $D = 8;

2. Then, for each choice from A, B, C, and D, add the value of the associated variable.
   
   

After you have stored that combined value, and later you read it back, and you want to decode the choices from the stored value...

To do that, you use the & operator (bitwise AND). For example, suppose the value you have stored and read back into a variable named $Answer is 5.

To decode Answer into the choices like this:

$intChoiceA = ($Answer & 1);
$intChoiceB = ($Answer & 2);
$intChoiceC = ($Answer & 4);
$intChoiceD = ($Answer & 8);

To get the choices as True|False, you can do it like this:

$bChoiceA = ($Answer & 1) > 0;
$bChoiceB = ($Answer & 2) > 0;
$bChoiceC = ($Answer & 4) > 0;
$bChoiceD = ($Answer & 8) > 0;

To get the choices as 0|1, you can do it like this (uses the PHP Ternary Operator:

$intChoiceA = (($Answer & 1) > 0) ? 1 : 0;
$intChoiceB = (($Answer & 2) > 0) ? 1 : 0;
$intChoiceC = (($Answer & 4) > 0) ? 1 : 0;
$intChoiceD = (($Answer & 8) > 0) ? 1 : 0;

Answer 2

By using bitwise operators in PHP you can do it like this:

$A = 1;
$B = 0;
$C = 1;
$D = 0; // input data

$i = $A | ($B<<1) | ($C<<2) | ($D<<3); // joined in one integer

// echo str_pad(decbin($i),4,'0',STR_PAD_LEFT); // bit test ok: 0101 ~ $D$C$B$A

// back conversion:
$A = $i&1;
$B = ($i&2) >>1;
$C = ($i&4) >>2;
$D = ($i&8) >>3;
echo "$A $B $C $D"; // prints "1 0 1 0"

Answer 3

You can use bitwise operations. Essentially, you achieve the effect by doing a bitwise OR on two or more numbers, and then checking if a number was OR'ed in by doing a bitwise AND on the number that you want to test for.

Example:

You want the user to select which languages they are fluent in. The options you present them are English, German, Russian, and Spanish.
First, start by defining the options in powers of 2:

$LANGUAGE_ENGLISH = 2;
$LANGUAGE_RUSSIAN = 4;
$LANGUAGE_GERMAN = 8;
$LANGUAGE_SPANISH = 16;

Let's say the user selects English and Russian. You would combine the options as follows:

$selected_options = 0; // we'll store the result in here
$selected_options = $LANGUAGE_ENGLISH | $LANGUAGE_RUSSIAN;
//It can also be express as:
//$selected_options |= $LANGUAGE_ENGLISH;
//$selected_options |= $LANGUAGE_RUSSIAN;

The $selected_options variable now contains our user's options. To check if an option was stored, you do a bitwise AND. If the result is 0, then the value was not stored. Otherwise, the value was stored.
Example:

if ($selected_options & $LANGUAGE_ENGLISH != 0)
    echo "English was selected";
else
    echo "English was NOT selected";

Requirements:

All numbers need to have non-overlapping bits. The easiest way to prevent overlaps is by only using numbers in powers of 2. For example, in the below table, 3 overlaps with 2, and cannot be used with 2. 1, however, does not overlap with 2 or 4, and can therefore be used with both.

1: 0001
2: 0010
3: 0011
4: 0100

Hope that helps