81000₂
Convert Decimal to Binary in PHP
What you’ll learn
- How division by two and remainders produce binary digits from right to left.
- Why you must handle zero and why the first method reverses collected bits.
- A second method using bit scan, plus a live preview.
Overview
Binary uses powers of two. To convert a nonnegative decimal integer into binary, repeatedly divide by 2 and track remainders 0 or 1.
Prerequisites
Basic loops, modulo, integer division, and strings in PHP.
Decimal to binary
Each binary digit is a coefficient on a power of two. Repeatedly taking n % 2 gives bits from least significant to most significant.
Division algorithm
For n ≥ 0, repeatedly write n = 2q + r with r in {0,1}. The remainders form binary digits from right to left.
Intuition
5101₂
Live Preview
Nonnegative integers in JavaScript safe range.
Algorithm (remainder method)
📜 Pseudocode
Pseudocode
function decimalToBinary(n):
if n == 0: return "0"
bits = []
while n > 0:
bits.append(n % 2)
n = floor(n / 2)
reverse(bits)
return join(bits)1
Divide by two and reverse bits
Classic approach: collect remainder bits, then reverse to print MSB-first.
php
<?php
function decimalToBinary(int $n): string
{
if ($n === 0) return "0";
$bits = [];
while ($n > 0) {
$bits[] = (string)($n % 2);
$n = intdiv($n, 2);
}
return implode('', array_reverse($bits));
}
echo decimalToBinary(15) . "\n";
echo decimalToBinary(0) . "\n";
?>2
Bit-scan from MSB to LSB
No reversal buffer needed. Start at highest set bit and read downward.
php
<?php
function toBinaryBitScan(int $n): string
{
if ($n === 0) return "0";
$out = '';
$started = false;
for ($b = 31; $b >= 0; $b--) {
$bit = ($n >> $b) & 1;
if ($bit || $started) {
$out .= $bit ? '1' : '0';
$started = true;
}
}
return $out;
}
echo toBinaryBitScan(15) . "\n";
echo toBinaryBitScan(64) . "\n";
?>Optimization
Built-in fast path. For nonnegative integers, decbin($n) is concise and reliable.
Fixed width. Use str_pad(decbin($n), 8, '0', STR_PAD_LEFT) when padding is required.
Interview: explain remainder logic first, then mention bit-scan or built-in.
❓ FAQ
The first remainder from n/2 is the least significant bit (parity). Each later remainder is the next higher bit. Printing from last remainder to first gives MSB to LSB.
The loop while n > 0 will not run, so you must handle n == 0 separately and return '0'.
It checks bits from a high position down to 0 and skips leading zeros. This avoids storing all remainders first.
For learning conversion, many tutorials restrict to nonnegative numbers. If you need signed representation, document whether you use absolute value or fixed-width two's complement.
Either minimal bits (no leading zeros) or fixed width like 8/16/32 bits, depending on problem requirements.
O(b) where b is number of output bits. For positive n, that's O(log2 n) in the remainder method.
🔄 Input / output examples
| Decimal | Binary (minimal) |
|---|---|
0 | 0 |
1 | 1 |
15 | 1111 |
64 | 1000000 |
Edge cases and pitfalls
Zero
n == 0
Return "0"; otherwise a plain while n > 0 loop returns empty output.
Negative
Policy choice
Choose absolute-value conversion or fixed-width two's complement and document it clearly.
Width
Minimal vs padded
Some tasks expect padded output like 00001111 instead of 1111.
⏱️ Time and space complexity
| Approach | Time | Extra space |
|---|---|---|
| Remainder + reverse | O(log n) | O(log n) |
| Bit scan | O(log n) | O(1) output aside |
Summary
- Use remainder and division by 2 to build bits.
- Always handle
n == 0separately. - Bit scan gives a neat MSB-to-LSB alternative.
Did you know?
Repeated division by 2 collects bits from least to most significant, so the usual classroom program prints the array backwards. A bit-scan loop can print from the MSB without an explicit reversal.
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