1. ## Number Bases

59 in base b converts to 113 decimal. What does 16 become ? I understand binary theory. Is there a formula similar to a binomial expansion that can be used ? If you can do 1 problem, like binary theory , all are easyish , I hope. Thanks.

2. Hello, stevieg!

Very little of what you posted makes any sense . . .

59 in base b converts to 113 decimal. .What does 16 become?
. . I assume that is: 16, base b.

I understand binary theory.
. . Do you mean binary numbers?
Is there a formula similar to a binomial expansion that can be used?
. . Do you mean (a + b)n?
If you can do 1 problem, like binary theory, all are easyish, I hope.
Thanks.

And there must be typo.

$59_b$ cannot equal $113_{10}$ . . . unless we can have: $b = 20\tfrac{4}{5}$

3. "59 in base b" means 5b+ 9 in decimal so your problem is telling you that 5b+ 9= 113. Solving that for b, 5b= 113- 9= 104 so that b=20 and 4/5. A fractional base is peculiar (as Soroban notes) but is theoretically possible.

But there turns out to be a very simple answer! Since 16 is less than that b, it would be written as 0b+ 16= 16, base b.

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