Binary

Binary

The system we usually use is decimal system, i.e. base 10, where we have 10 digits to describe any number (0,1,2,3,4,5,6,7,8,9). When keeping track of amounts larger than 9, multiple digits are necessary, where each digit represents a power of 10. For example, the number $1067$ can be expanded to make this explicit:

$1067=1\cdot 10^{3}+0\cdot 10^{2}+6\cdot 10^{1}+7\cdot 10^{0}$

Now consider a numbering system where each digit represents a power of 2.

Binary Addition

add stuff here

$0$

	${\begin{aligned}(\left\vert \psi \right\rangle )^{*}&=\left({\begin{array}{c}\alpha \\\beta \end{array}}\right)^{*}\\&=\left({\begin{array}{c}\alpha ^{*}\\\beta ^{*}\end{array}}\right)\\&=\alpha ^{*}\left\vert 0\right\rangle +\beta ^{*}\left\vert 1\right\rangle .\end{aligned}}$	(C.1)