PHP How to Convert Binary to Decimal Number

In PHP, convert binary to decimal using bindec() function like bindec('1010') which returns 10.

Examples

Input1010

Output10

Input11111111

Output255

Input0

Output0

How to Think About It

To convert binary to decimal, think of each binary digit as a power of 2 starting from the right (0th power). Multiply each digit by 2 raised to its position index and add all results to get the decimal number.

Algorithm

1

Get the binary number as a string input.

2

Start from the rightmost digit and assign it position 0.

3

For each digit, multiply it by 2 raised to the power of its position.

4

Add all these values together to get the decimal number.

5

Return the decimal number.

Code

php

<?php
$binary = '1010';
$decimal = bindec($binary);
echo $decimal;
?>

Output

10

Dry Run

Let's trace binary '1010' through the code

1

Input binary string

binary = '1010'

2

Convert using bindec

bindec('1010') calculates decimal

3

Output decimal

decimal = 10

Binary Digit	Position	Value (digit * 2^position)
0	0	0 * 2^0 = 0
1	1	1 * 2^1 = 2
0	2	0 * 2^2 = 0
1	3	1 * 2^3 = 8

Why This Works

Step 1: Using bindec function

PHP's bindec() converts a binary string directly to decimal by internally calculating powers of 2.

Step 2: Binary digit positions

Each binary digit represents a power of 2 based on its position from right to left starting at 0.

Step 3: Summing values

Multiplying each digit by its power of 2 and summing all gives the decimal equivalent.

Alternative Approaches

Manual calculation with loop

php

<?php
$binary = '1010';
$decimal = 0;
$length = strlen($binary);
for ($i = 0; $i < $length; $i++) {
    $bit = $binary[$length - $i - 1];
    $decimal += $bit * pow(2, $i);
}
echo $decimal;
?>

This method shows the calculation steps but is slower and more code than bindec.

Using base_convert function

php

<?php
$binary = '1010';
$decimal = base_convert($binary, 2, 10);
echo $decimal;
?>

base_convert converts between bases but returns a string; bindec returns an integer.

Complexity: O(n) time, O(1) space

Time Complexity

The conversion scans each binary digit once, so time grows linearly with input length.

Space Complexity

Only a few variables are used, so space is constant regardless of input size.

Which Approach is Fastest?

Using bindec() is fastest and simplest; manual loops are slower but educational.

Approach	Time	Space	Best For
bindec()	O(n)	O(1)	Quick and easy conversion
Manual loop	O(n)	O(1)	Learning how conversion works
base_convert()	O(n)	O(1)	Converting between any bases