Errors Accuracy and Roundoff

1. Binary
   1. Convert binary to deciman (>1 and <1)
2. Floating point representation
   1. why is it call that (float point representation)?
   2. how are 1.001E3 and 2.2E-1 added?
   3. What are the parts of a floating point number including their names?
3. Precision
   1. What is the relative error (machine precision) for doubles on a computer?
   2. How many bits are in a byte?
   3. How many bytes and bits are in a double?
   4. In math, we have $\mathbb{N,,Z,,Q,,R,,C}$. Which do we have naturally on computers?
   5. Is $a+b+c$ the same as $a+c+b$? Why?
4. Roundoff error analysis
   1. What is 1/10 in binary? (Why is that interesting?)
   2. Whis is best: $a^2-b^2$ or $(a-b)(a+b)$?
   3. Which calculation should make you more nervous and why: $\prod_ix_i$, $\sum_ix_i$?
   4. Why is subtracting two nearly equal numbers bad?