A binary full adder. Inspired by The Reasoned Schemer.

binary-adder.php

<?php

function bit_xor($x, $y) {
    return intval($x xor $y);
}

function bit_and($x, $y) {
    return intval($x && $y);
}

// [result, carry-out]
function half_adder($x, $y) {
    return [
        bit_xor($x, $y),
        bit_and($x, $y),
    ];
}

// [result, carry-out]
function full_adder($x, $y, $cin) {
    list($w, $xy) = half_adder($x, $y);
    list($result, $wz) = half_adder($w, $cin);

    return [
        $result,
        bit_xor($xy, $wz),
    ];
}

// 4-bit full-adder
$xs = array_reverse([1, 0, 1, 0]);
$ys = array_reverse([1, 0, 0, 1]);
$carry = 0;

$sum = [];

foreach (range(0, 3) as $i) {
    list($bit, $carry) = full_adder($xs[$i], $ys[$i], $carry);
    $sum[] = $bit;
}
$sum[] = $carry;

echo json_encode(array_reverse($sum))."\n";