Computing and Informatics: Conversion of a number from any system to the decimal system

Let us study the formation of the number 1970 in the decimal system.

\begin{array}{l}
{(1970)_{10}}\, = \,1\,x\,{10^3} + 9\,x\,{10^2} + 7\,x\,{10^1} + 0\,x\,{10^0}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \,1000 + 900 + 70 + 0\,\,\, = \,\,1970
\end{array}

Convert binary number (111)₂ into the decimal system

{(111)_2}\, = \,1\,x\,{2^2} + 1\,x\,{2^1}\, + 1\,x\,{2^0}\,\, = \,\,4 + 2 + 1\,\, = \,\,{(7)_{10}} 

Convert octal number (1654)₈ into the decimal system

{(1654)_8}\, = \,1\,x\,{8^3} + 6\,x\,{8^2} + 5\,x\,{8^1} + 4\,x\,{8^0}\,\, = \,\,512 + 384 + 40 + 4\,\,\, = \,\,{(940)_{10}}  

Convert Hexa-decimal number (123)₁₆ to the decimal system

{(123)_{16}}\, = \,1\,x\,{16^2} + 2\,x\,{16^1} + 3\,x\,{16^0}\,\, = \,\,256 + 32 + 3\,\,\, = \,\,{(291)_{10}}  

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