$1.$ 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.

$2.$ Please do error checking for input.

i$.$ Wrong base, allow user to renter correct base.

ii$.$ Wrong number for each base and allow to renter correct number for the base.

Example:

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

Please enter a number: $31$

Binary: $11111$

Decimal: $31$

Hexadecimal: $1$F

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

Please enter a number: $31$

Binary: $11111$

Decimal: $31$

Hexadecimal: $1$F

Please enter a base $(2/10/16)$: $8$

Error: Illegal Base

Please enter correct base

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

Please enter a number: $1201$

Error: Illegal digit for the base

Please enter correct number for the base

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

Please enter a number: $23$

Binary: $100011$

Decimal: $35$

Hexadecimal: $23$