This article explains PHP's binary operators and base conversion. While many resources briefly cover these topics, a deeper understanding of number theory is crucial for effective use. This article provides that foundational knowledge.

Key Concepts:

• Understanding number theory and base conversion is essential for using PHP's binary operators effectively. Familiarity with binary digits is key.
• PHP offers functions like decbin(), bindec(), decoct(), octdec(), dechex(), hexdec(), and base_convert() for simplifying base conversions.
• PHP's bitwise operators (&, |, ^, ~) manipulate binary values at the bit level, creating new values from binary representations.
• Binary operators enable bit masking in PHP, isolating and manipulating specific bits within binary numbers. This is useful when binary numbers represent checklists or tallies.

Number Theory and Base Conversion:

Our familiar base-10 (decimal) system uses packages and containers. Units are bundled in multiples of 10. Once a container is full (9 units), the contents are bundled and moved to the next container to the left.

Other base systems exist. The key is that each container's limit is one less than the base. For example:

• Base-8 (octal): Each container holds up to 7 units.
• Base-16 (hexadecimal): Each container holds up to 15 units (A-F represent 10-15).
• Base-2 (binary): Each container holds either 0 or 1 unit.

In binary, each container is either full (1) or empty (0). This is crucial for understanding bitwise operations.

Binary numbers can be visualized as checklists: 1 is a checkmark, 0 is the absence of a check.

PHP Conversion Functions:

PHP provides built-in functions for base conversion:

• decbin(): Decimal to binary.
• bindec(): Binary to decimal.
• decoct(): Decimal to octal.
• octdec(): Octal to decimal.
• dechex(): Decimal to hexadecimal.
• hexdec(): Hexadecimal to decimal.
• base_convert(): Conversion between arbitrary bases.

Example using decbin(), decoct(), dechex():

<?php
$num = 21;

echo "Decimal value: $num\n";
echo "Binary value: " . decbin($num) . "\n";
echo "Octal value: " . decoct($num) . "\n";
echo "Hexadecimal value: " . dechex($num) . "\n";
?>

Example using base_convert():

<?php
$num = 21;

echo "Decimal value: $num\n";
echo "Base-7 value: " . base_convert($num, 10, 7) . "\n";
echo "Base-11 value: " . base_convert($num, 10, 11) . "\n";
?>

Bitwise Operators:

• Bitwise-AND (&): Returns 1 only if both corresponding bits are 1.
• Bitwise-OR (|): Returns 1 if at least one of the corresponding bits is 1.
• Bitwise-XOR (^): Returns 1 if only one of the corresponding bits is 1.
• Bitwise-NOT (~): Inverts all bits (0 becomes 1, 1 becomes 0).

Masking with Binary Operators:

Bitwise operators are useful for masking, isolating specific bits in binary numbers used as checklists.

<?php
// ... (Example code for masking is omitted for brevity, but the original example can be included here) ...
?>

This article provides a comprehensive overview of number theory, base conversion, and the practical application of PHP's binary operators, including bit masking. The provided examples illustrate how to use these concepts effectively in PHP programming.

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