# $25_r = 23_{10}$ solve for the base r

first of all this is a homework question and I don't want the solution. I just want a reference to how to solve similar questions like this. I believe it's explained my course textbook, "Computer Organization & Architecture: Themes and Variations" but I currently cannot afford the textbook.

Here's the question:

For each of the following numbers, state the base in use; that is, what are the values of r, s, and t?

a. $25_r = 23_{10}$

b. $1001_s = 19684_{10}$

c. $1011_t = 4931_{10}$

I recognize it's similar to solving an equation. I'm guessing I have to find r, s and t and they will be a specific base that matches the base ten number. I tried searching online for similar questions but I'm not sure what to search for so I have no clue where to start for solving these equations.

Any help would be appreciated.

• 1. Can you identify a more general conceptual question that you want information on? That will make this more useful to others in the future. 2. Book recommendation requests are generally off-topic for this site. (e.g., meta.cs.stackexchange.com/q/303, meta.cs.stackexchange.com/q/874/755). A request for a cheaper textbook for computer architecture is off-topic, but if you can identify a specific topic/concept, it might be on-topic. 3. What have you tried? What research have you done? Where have you looked? We expect you to make a serious effort on your own to find resources.
– D.W.
Jan 29, 2015 at 1:17
• This question seems to be covered by Wikipedia, e.g., en.wikipedia.org/wiki/Radix and en.wikipedia.org/wiki/Positional_notation. If the answer to your question can be found on Wikipedia, that often suggests you need to put more effort into researching your question on your own before asking, and it typically means your question isn't a good fit for this site.
– D.W.
Jan 29, 2015 at 1:20

Consider $25_{10}$. The number can be written as $5 \cdot 10^0 + 2 \cdot 10^1$.
How can $25_{r}$ be written?