Question $2$:

A software engineer is developing a microcontroller that communicates using different number systems. The engineer needs to ensure that the microcontroller correctly handles inputs and outputs in binary, octal, and hexadecimal formats. The engineer tests this by converting and performing arithmetic operations in different base systems to verify that the microcontroller is functioning correctly.

Convert the following numbers to the indicated base systems and perform the operations:

$1.$ Convert $27($denary$)$ to binary, octal, and hexadecimal.

$2.$ Add the binary numbers $101101$ and $11101.$

$3.$ Multiply the octal numbers $65$ and $47.$