# Thread: changing base of log without evaluating?

1. ## changing base of log without evaluating?

Express $\displaystyle 101101_2$ in base 4

okay im not sure what the question means but the answer was $\displaystyle 231_4$.

2. Hello, requal!

Express $\displaystyle 101101_2$ in base 4 without evaluating.

Answer: $\displaystyle 231_4$

The usual way is to convert the number to base-ten, then to base-four.

But they expect us to convert to base-four directly.

This can be done by breaking the number into two-digit groups: .$\displaystyle 10\;11\;01$

$\displaystyle \text{Then convert each each pair: }\:\underbrace{10_2}_{\downarrow}\:\underbrace{11_ 2}_{\downarrow}\:\underbrace{01_2}_{\downarrow}$
. - . - . . . . . . . . . . . . . . . $\displaystyle 2 \quad\;\;\: 3\quad\;\:\:1$

Therefore: .$\displaystyle 101101_2 \;=\;231_4$

3. actually I think they want us to convert to base 10 than to base 4- can you show me how to do that because I kinda dont understand the above answer.

4. Originally Posted by requal
actually I think they want us to convert to base 10 than to base 4- can you show me how to do that because I kinda dont understand the above answer.
$\displaystyle 101101_2 = 1 \times 2^0 + 0 \times 2^1 + 1 \times 2^2 + 1 \times 2^3 + 0 \times 2^4 + 1 \times 2^5 = \, ....$