Tiny tutorial regarding converting base X to decimal(and testing LateX)

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Tiny tutorial regarding converting base X to decimal(and testing LateX) - mad1231999 - 05-10-2013

Let the digits of the number be contained in the n-dimensional vector a, like this:
$a = \left[1 \vspace{5 mm} 0 \vspace{5 mm} 0 \vspace{5 mm} 1 \vspace{5 mm} 1 \vspace{5 mm} 1 \vspace{5 mm} 0 \vspace{5 mm} 1\right]$
which is equivalent of the binary number 10011101.

Given the base $b$ (2 in this case), the number in decimal can be found using the following equation:

$x = \sum_{i=1}^{n}a_{(n-i)} \cdot b^{(i-1)}$

So we can conclude, that this is true:

$x = \sum_{i=1}^{8}{a_{(n-i)} \cdot 2^{(i-1)}} = 157$

RE: Tiny tutorial regarding converting base X to decimal - Guy1234567890 - 05-10-2013

Fancy!

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - David - 05-11-2013

Wait, wut?

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - EDevil - 05-11-2013

(05-11-2013, 10:39 AM)David Wrote: Wait, wut?

Same here. We're probably not that far into logic & formula's Sad

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - JayJuly - 05-11-2013

Lol, nice use of sigma notation to confuse people Wink

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - Thor23 - 05-11-2013

I think you've got your vector backwards. If you're indexing the digits like in a typical array, the index would be increasing from left to right, so you would get 185 not 157. You'd have to use $a_(_9_-_i_)$ to get that.

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - mad1231999 - 05-12-2013

Thank you, didn't think about that. Fixed.

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - VirtualPineapple - 05-13-2013

*Hits, 'That was easy' button*

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - Xeomorpher - 05-13-2013

Oi, leave my buttons alone!

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - David - 05-26-2013

I understood it until you brought the equation, maybe I should go to school for a few more years.

RE: Tiny tutorial regarding converting base X to decimal(and testing LateX) - fl3tching101 - 06-20-2013

Uhm, lol that's like the most complicated equation ever for converting binary to decimal. I suppose it's cool because it works with any base, but it's kind of useless to memorize that complex series summation when you could probably do the conversion faster using simpler methods to a certain amount of digits. This would be pretty useful for a program to do base conversions though Tongue

Oh, and for those that are confuzled by that, it's sigma notation for a series, in this case a sum of a series. Not sure when you usually learn series, but we learned them in our Algebra II class, however we were working in Advanced Algebra. So I suppose it's either an Algebra II or Advanced Algebra concept. Basically all it is saying is to plug in i and increment until n is reached and add up all of those sums. You plug in 1, solve, plug in 2, solve, etc and add up all of the solutions.