Starting out with a value and modifying it piecemeal as you go through a list of something, which you do with $ret and the digits in both functions, is an ideal candidate for List::Util's reduce function.

use List::Util qw( reduce );

sub bin2dec {
    my ( $str ) = @_;
    reduce { mul2( $a, $b ) } "", split //, $str;
}
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Here, in the first iteration, $a is the empty string from the list passed to reduce, and $b is the first digit. The return value of the block is passed back to the block as $a in the next iteration, while $b goes through the all the remaining values from the list one by one.

$add_one_f I'd rename as $have_overflow, which documents intent rather than implementation. And if you only use it as a boolean, you don't need to initialize it either.

The for(;;) loop isn't necessary, you don't use the index anywhere, you just extract each corresponding character once. So you could rewrite that much more clearly as for( reverse split //, $str ). Then it could be turned into a reduce in the same way as above, but since you're just accumulating characters onto the front of a string, you are better served with a join reverse map.

sub mul2 {
    my ( $str, $have_overflow ) = @_;

    my $ret = join '', reverse map {
        my $c = $_ * 2 + ( $have_overflow ? 1 : 0 );
        $have_overflow = ( $c >= 10 );
        ( $c % 10 );
    } reverse split //, $str;

    ( $have_overflow ? 1 : '' ) . $ret;
}
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You could even get rid of the out-of-band overflow check at the bottom if you rearrange things a little:

sub mul2 {
    my ( $str, $have_overflow ) = @_;
    join '', reverse map {
        my $c = $have_overflow ? 1 : 0;
        $c += $_ * 2 if length;
        $have_overflow = ( $c >= 10 );
        # return a zero char only if not at top of string
        ( $c % 10 ) or ( length() ? 0 : '' );
    } reverse '', split //, $str;
}
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But in this case I find it obfuscates more than it reduces redundancy.

Incidentally, the ( $have_overflow ? 1 : '' ) above is a no-op if $have_overflow is a boolean like in this case, since 1 and the empty string are what the boolean ops return in Perl for true and false respectively. So that could be written $have_overflow . $ret, though that lacks the the benefit of documented intent.

Makeshifts last the longest.