Digital representation of information

In logic circuits information is represented as eletronic signals that represent the voltage level in a circuit. This signals are usually denoted as $0$ and $1$. Binary numbers can be converted to decimal using the following formula:

$$V(B)=b_{n-1}\times 2^{n-1}+b_{n-2}\times 2^{n-2}...b_1\times 2^1+b_0\times 2^0$$

Converting a decimal number to a binary is not that simple, as we have to divide the decimal number by $2$ multiple times like in the example:

$$\begin{array}{ccc}& \text{Remainder}& \\ 857÷2=428& 1& \text{LSB}\\ 428÷2=214& 0& \\ 214÷2=107& 0& \\ 107÷2=53& 1& \\ 53÷2=26& 1& \\ 26÷2=13& 0& \\ 13÷2=6& 1& \\ 6÷2=3& 0& \\ 3÷2=1& 1& \\ 1÷2=0& 1& \text{MSB}\end{array}(857{)}_{10}=(1101011001{)}_2$$

In Chapter 3 we return to this subject when discussing the representation of negative numbers.