# How to convert base 7 to base 19 directly

Is it possible to convert base 7 to base 19 directly without first converting to base 10 ?

If so, what is the algorithm ?

• Yes­­­­­­­­­­­­ – evil999man Apr 12 '14 at 11:13
• Yes. 10 isn't special; it's just the number after 9. It only seems special because we've chosen it as the usual base we work in. – user2357112 supports Monica Apr 12 '14 at 11:13
• The algorithm is the same one you'd use to convert from base $7$ to base $10$, except for the obvious. – Jack M Apr 12 '14 at 11:15
• Same exact algorithm you'd use for converting from base 10 to base 19, except with all the 10s switched out for 7s. – user2357112 supports Monica Apr 12 '14 at 11:15
• @Cemre Why didn't you Google first what will you ask before posting your question here? Anyway, answer of your question may refer to this link. I hope this helps. – Tunk-Fey Apr 12 '14 at 11:22

1. Work in base nineteen. Calculate the powers of $7$ in base nineteen, multiply them by the base-7 digits of the original number, add together.
2. Work in base seven. Start with your original number, successively divide by nineteen (that is, $25_7$), and remember the remainders; these become your base-nineteen digits.