Write a program using C$++$ to convert from binary, octal, hexadecimal and decimal numbers $($please $**$make sure to show both integers and floating point numbers$***$ for example, program need to convert decimal $25\mathrm{.}4$ to binary $11001\mathrm{.}01100).$Your program would$*$ ask the users to enter a number in binary or decimal$*$ ask the users what type$$ of number it is $($binary or decimal$)*$ check to make sure the number is legal $($a decimal number contains only $0-9).$ If the number is not legal, it should error out!$*$ If the number is legal, convert the number to the other $3$ types $($Hint: There are a total of $4$ types: binary, octal, hexadecimal, decimal$)$Your program needs to do basic error$-$checkingYou CANNOT use ANY pre$-$defined built$-$in functions to do the conversion such as the following!!Integer.toString$($n$,8)//$ decimal to octalInteger.toString$($n$,2)//$ decimal to binaryInteger.toString$($n$,16)//$decimal to Hex