Using C$++,$ Write a program to covert a number among $3$ numbering system $$ binary, decimal, and hexadecimal. Your program will ask user to enter a number with the base and convert to the other $2$ different bases. Please do error checking for input $($ the number and the base$).$

Example:

Please enter a base $(2/10/16)$: $10$

Please enter a number: $31$

Binary: $11111$

Decimal: $31$

Hexadecimal: $1$F