Binary number to decimal conversion

Binary numbers are the integral part of digital logic.

The rules of binary numbers translation to decimal numbers, that we used to operate with, are very similar to the decimal rules.

Binary logic represent two digits, called bits, and the values are 1 and 0. Binary numbers with the structure like $a_n{a}_{(n–1)}\dots a_1{a}_0$ are contracted by bonding the bit values with the following expression: $(–1{)}^{\left(a_n\right)}{{\sum }_{(i=0)}}^{(n–1)} a_i{2}^i.$ Here $a_n$ can be 1 or 0.

Example: 11001. Here $a_0=1, a_1=0, a_2=0, a_3=1, a_4=1$.

Using formula above $11001=(–1{)}^1(2^0*1+2^1*0+2^2*0+2^3*1)=–9$