Binary to Decimal Right of The Binary Point

Question

I need to convert 10000000110.011 to decimal. The first part I fully understand, 2^10 + 2^2 + 2^1 = 1030. Wolfram Alpha confirmed that 1030 is correct. But for the right of the binary point, WA gives me an answer of .375, and I'm really confused how this was calculated. I tried searching here and Google, some applicable stuff, but nothing that made any sense for whatever reason. Can anyone offer me a quick step-by-step for doing this last part?

Thanks!

Okay thanks, but where is the 1/4th and the 1/8th coming from? — bnr32jason, Jan 18 '16 at 02:38
Think about what the notation means: The positions left of the decimal point correspond to $2^{+1}, 2^{+2}$ and so on. What do the positions right of the decimal point correspond to? — , Jan 18 '16 at 02:40
2^-1, 2^-2, etc? So do I add a zero in front of the first zero to get .0011 so then it would be 2^-2 and 2^-3? — bnr32jason, Jan 18 '16 at 02:42

score 1 · Accepted Answer · answered Jan 18 '16 at 03:08

$\color\green1\color\red0\color\red0\color\red0\color\red0\color\red0\color\red0\color\red0\color\green1\color\green1\color\red0.\color\red0\color\green1\color\green1=$

$\color\green1\cdot2^{10}+$

$\color\red 0\cdot2^{ 9}+$

$\color\red 0\cdot2^{ 8}+$

$\color\red 0\cdot2^{ 7}+$

$\color\red 0\cdot2^{ 6}+$

$\color\red 0\cdot2^{ 5}+$

$\color\red 0\cdot2^{ 4}+$

$\color\red 0\cdot2^{ 3}+$

$\color\green1\cdot2^{ 2}+$

$\color\green1\cdot2^{ 1}+$

$\color\red 0\cdot2^{ 0}+$

$\color\red 0\cdot2^{-1}+$

$\color\green1\cdot2^{-2}+$

$\color\green1\cdot2^{-3}=$

$1030.375$

Binary to Decimal Right of The Binary Point

1 Answers1