Write a program using C$++$to convert from binary, octal, hexadecimal and decimal numbers $($both integers and floating point numbers$).$Your program woud $1)$ ask the users to enter a number in binary or decimal $2)$ ask the users what type$$ of number it is $($binary or decimal$)3)$ 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!$4)$ 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$).$Program needs to do basic error$-$checking NOTE: You 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 You must use your functions$/$methods$.$ Think iteration $($loops$)$ or recursion. You must use the addition$/$subtraction method or the division$/$multiplication method