Would the following help you?  It's my attempt to provide a pictorial representation of what's happening:

use strict;
use warnings;

my $value = 51;

# Accumulate binary digits ("bits")
my @bits = ( );
foreach my $place (0 .. 7) {
    my $nextbit = mask_off_bit($value, $place);
    push @bits, $nextbit;
}

# Display each bit
printf "\nNumber %3d in binary is:  ", $value;
map { print "$_" } reverse @bits;
print "\n";

# Test the results against good ol' printf
printf "   Which is the same as:  %08b\n", $value;


sub mask_off_bit {
    my ($num, $place) = @_;
    my $mask = 1 << $place;                     # Same as 2 ** $place
    my $mstr = " " x (8 - $place) . "^";        # Graphic representati
+on
    printf " Num %3d:  0b%08b\n", $num, $num;   # Number in decimal & 
+binary
    my $bit = ($mask == ($num & $mask))? 1: 0;  # Next bit is one or z
+ero
    printf "Mask %3d:   %s => bit %d\n", $mask, $mstr, $bit;
    return $bit;
}
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The above code is masking off each bit, using a mask of 1, 2, 4, 8, etc. in the line:

    my $bit = ($mask == ($num & $mask))? 1: 0
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