Hello, merlyn. Basically, you are right here. Numbers are one thing, and representations are an other, so saying "convert a decimal number to a binary one" might not be a very precise phrase. I admit that I may be prone to this kind of error sometimes.

I, however, have to disagree with your reply in this particular case. Most solutions in this thread, or indeed, most solutions that would come into your mind if someone asks this questions indeed work by first converting the decimal representation of a number to an internal form, than converting that number to binary form. The internal for may be based on binary, or it may be based on decimal, but this is not important to the user. (If I'm not much mistaken, binary representation of bignums are used in ruby and mathematica; decimal ones in perl's Math::BigInt, dc or bc.)

The paricular node you've replied to, however, is different. I am not using any internal representations, nor do I use readily provided (by the CPU, Perl, a module, or any other software) arithmetic operations on those. If you read my code, you'll see that the numbers here are always in the form of a srting, more precisely either a decimal or a binary representation of it. (You may count the subroutines on the stack as a different representation if you really want.) All I'm doing with these representations is string operations (provided by perl), and a single indexing an array by a digit. Again, I never convert neither the whole number, nor parts of it to numeric forms understood by the cpu or perl or any perl module, I am implementing all numeric operations by hand.

You also mention that you don't see any decimal operations in this code. This is because they are not needed: to convert from one representation of a number to an other, you can either do divisions on the first representation, or multiplications on the other. I have chosen the second one, so I do only binary operations; the only decimal operation I do is take the decimal number to digits, and index a lookup array with each.

Note that this decision of using multiplication or division is usually given by what representation of numbers you use internally. With current cpus, you store numbers in (binary) fixnums, and we can do fast arithmetic on those, so we use binary multiplication to convert from decimal to fixnum (see perl-5.8.5/toke.c:8047), and binary division to convert fixnum to decimal (see perl-5.8.5/sv.c:8956). A bignum library with decimal representation would, of course, use decimal division to convert to binary (bc-1.06/lib/number.c:bc_out_long:1521), and decimal multiplication to convert from binary (bc-1.06/bc/execute.c:push_constant:644). (These could be mixed in theory, even a decimal bignum library could include some binary bignum operations or vice versa, if that helped converting numbers faster.)

If you look at my program like this, this program does arithmetic operations in binary, so its internal form is binary. Thus, if you don't like the name dec2bin, it should really be called dec2num, not num2bin, as it converts from decimal to internal numeric form. I, however, don't think I use either binary or decimal as an internal numeric form, so I think I can call it dec2bin.

As for the unchecked regexp matches, you are right, I should indeed chack them. I am, however, lazy, and for a quick demonstration such as this, didn't really care about that. If you give a non-numeric argument to dec2bin, the regexp match of $dec=~/(\d)/g will fail, and the value of $1 will be undefined (not undef). This is a bug, and I'll correct it.

Update: next time, I'll think before I post something.