Question $1$: Write an Octave function that takes a decimal number as input and returns its binary representation as a string. The function must conform to the following requirements:

It iteratively divides the number by $2$ and records the remainders, which form the binary representation in reverse order. The function then reverses the binary string before returning it$.$

i$.$ It must not use the dec$2$bin Octave function or any other built$-$in Octave functions for converting numbers to binary. Utilize only basic arithmetic operations and string manipulation.

ii$.$ Use dec$2$bin function to test if the calculated string is the same

iii. Use a WHILE loop to convert number to binary string