Question

11101010100110.0101010111 base 2 (convert this number to base 4)

Answer 1

3222212.11113

Explanation:

First, you should take care of the fractional separator (the dot) so we split the problem in two parts: one for the integer and other for the fractional part.

Since 4 is a power of 2, we can just take two digits from the orignal number and asign it to its corresponding number in base 4:

`\left[\begin{array}{cc}Binary&Base 4\\00&0\\01&1\\10&2\\11&3\end{array}\right]`

Start with the fractional part from the fractional point to the right:

`\left[\begin{array}{ccccc}01&01&01&01&11\\1&1&1&1&3\end{array}\right]`

Then do the same to the integer part starting from the fractional point to the left.

`\left[\begin{array}{ccccccc}11&10&10&10&10&01&10\\3&2&2&2&2&1&2\end{array}\right]`

By joining them together, we obtain the response.