Product with floating point [closed]

I was studying the product with floating point and I saw this example. I made the translation, sorry if something is not grammatically correct.

![enter image description here][1]

• The book is wrong. As you write, $2.5\times 12.125 = 30.3125$. – Yuval Filmus Nov 7 '14 at 1:06
• The problem is that with the outcome of the product x1*x2 that I put, I dont get to 30.3125. So I am doing something wrong too. – Richy Nov 7 '14 at 1:14
• Why not? $(11110.0101)_2 = (30.3125)_{10}$. – Yuval Filmus Nov 7 '14 at 1:15
• Don't use images as main content of your post. This makes your question impossible to search and inaccessible to the visually impaired; we don't like that. Please transcribe text and maths (note that you can use LaTeX) and don't forget to give proper attribution to your sources! – Raphael Nov 7 '14 at 8:35
• This question consists of scanned text and is thus unsearchable. It can be reopened if the text is posted as text. – Gilles 'SO- stop being evil' Nov 7 '14 at 14:20

Here is the complete calculation: \begin{align*} &2.5 = (.101)_2 \times 2^2 \\ &12.125 = (.1100001)_2 \times 2^4 \\ &(.101)_2 \times 2^2 \cdot (.1100001)_2 \times 2^4 = (.0111100101)_2 \times 2^6 = (.111100101)_2 \times 2^5 \\ &(.111100101)_2 \times 2^5 = 30.3125 \end{align*} Ignore what the book says, and just make sure that you understand why this calculation works out.
• That's because I multiply numbers rather than strings of digits. My numbers have meaning. Try calculating $.1\times .1=.01$ – even though $1\times 1=1$, you get the extra zero. – Yuval Filmus Nov 7 '14 at 14:53