05-10-2013, 03:49 PM
(This post was last modified: 05-13-2013, 07:46 PM by mad1231999.)
Let the digits of the number be contained in the n-dimensional vector a, like this:
![](http://www.forkosh.dreamhost.com/mimetex.cgi?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
(2 in this case), the number in decimal can be found using the following equation:
![](http://www.forkosh.dreamhost.com/mimetex.cgi?x = \sum_{i=1}^{n}a_{(n-i)} \cdot b^{(i-1)})
So we can conclude, that this is true:
which is equivalent of the binary number 10011101.
Given the base
So we can conclude, that this is true: