a$)$ Develop a Matlab function decima$12$binary that converts a decimal number $x$ into a binary floating point number in enginecring notation. The function shall take as input the decimal number $x$ and the number of bits to be used in the mantissa $N($excluding the hidden bit$)$ and shall output the vector m containing the $N$ mantissa bits $($excluding the hidden bit$),$ the exponent $p$ in decimal of the binary floating point number in engineering notation, and the remainder r of the transformation. Do not print out results to screen within the function.

b$)$ Using the function decimal$2$binary convert the decimal number $0\mathrm{.}1$ to a binary foating point number in engineering notation using $10,50,$ and $60$ mantissa bits and report the remainders.

c$)$ Why does Matlab report the remainder as $0$ when $60$ mantissa bits are used, even though infinitely many bits would be required to convert the decimal number $0\mathrm{.}1$ into a binary foating point number?