Add binary

You are given two binary numbers, $a and $b. Write a script to simulate the addition of the given binary numbers. The script should simulate something like $a + $b. (operator overloading)

Examples

Example 1
Input: $a = 11; $b = 1;
Output: 100

Example 2
Input: $a = 101; $b = 1;
Output: 110

Example 3
Input: $a = 100; $b = 11;
Output: 111

Analysis

My feeling is that the clearest way to do this is to write 2 functions, dec_to_bin() and bin_to_dec(). The challenge can then be addressed with

$result = dec_to_bin(bin_to_dec($a) + bin_to_dec($b));

The 'dec' format is a number stored in Perl's or the underlying machine's native format, and the 'bin' format is a series of 0s and 1s representing the individual binary digits of the number.

The dec_to_bin function is readily available in Perl as
sprintf('%b', $a), but bin_to_dec is a little harder. I had hoped for eval(0b$arg), but sadly that doesn't work.

I am sorry that the 'Try it' feature is currently working very slowly or not at all owing to some issue with my web hosting provider.

Try it 

#!/usr/bin/perl

# Peter Campbell Smith - 2021-11-22
# PWC 140 task 1

use v5.20;
use warnings;
use strict;

my (@tests, $a, $b);

# pairs to be added
@tests = (11, 1,   101, 1,   100, 11,   10101, 1010,   0, 111,   1111111111, 1111111111);

while (1) {
    
    # pick off next pair
    $a = shift @tests;
    last unless length($a);
    $b = shift @tests;
    
    # give answer
    say qq[$a + $b = ] . dec_to_bin(bin_to_dec($a) + bin_to_dec($b));
}

sub bin_to_dec {
    
    # converts a string of 0s and 1s to a decimal value
    my ($arg, $result);
    
    $arg = $_[0];
    $result = 0;
    
    # process digits
    while ($arg =~ m|^(.)(.*)$|) {
        $result = 2 * $result + $1;
        $arg = $2;
    }
    return $result;
}

sub dec_to_bin {
    
    # coverts a decimal number to binary representation
    return sprintf('%b', $_[0]);
}

10 lines of code

Output from script

11 + 1 = 100
101 + 1 = 110
100 + 11 = 111
10101 + 1010 = 11111
0 + 111 = 111
1111111111 + 1111111111 = 11111111110