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A book taught me a way to transform a number to another scale of notation. For example:

1: To transform $34268$ from the scale of $5$ to the scale of $11$: Rule - Divide successively by the new radix.$$\begin{align*} & 11|34268\\ \hline & \hspace{5mm}11|1343-t \\\hline & \hspace{10mm}11|40-3\\\hline & \hspace{18.2mm}1-9\end{align*}$$ Result: $193t$ in which $t$ stands for $10$.

Problem is, I'm not sure what the author did. It seems like they were dividing $34268$, but the remainder that I get is no where near $1343$.

Question:

  1. What was the follow-through the author did?
  2. How does this adress the question of $34268$ in the scale of $11$?

1 Answers 1

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34268 is supposed to be a number in scale 5. Now this is REALLY strange since in that scale, 6 and 8 should never show up. Nevertheless, converting to decimal numbers, we have $"34268" = 8+6*5+2*5^2+4*5^3+3*5^4= 2463$

In scale 11, we have $"193t" = 10 + 3*11+9*(11)^2 + (11)^3 = 2463$

This answers your second question.

Answering your first question:

what the author did was successively divide by the highest power of 11, and continuing this procedure for the remainder (as in standard written division). What is hard to see is that he applied that procedure for a base 5 number.

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    I don’t understand. Can you provide an example? I don’t see how he divided successively for a base five number in base 11. – 2018-03-28
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    @Crescendo There is a general explanation of 3 main methods (with examples) in http://www.deimel.org/comp_sci/conversion.htm – 2018-03-28