Suppose you have a pizza shop and you advertise a sale for a $4-$topping pizza.

Your $14$ toppings are listed below:

$$ Pepperoni

$$ Black Olives

$$ Green Olives

$$ Peppers

$$ Onions

$$ Anchovies

$$ Mushrooms

$$ Sausage

$$ Eggplant

$$ Basil

$$ Ham

$$ Pineapple

$$ Meatball

$$ Pesto

$($a$)$ Count the number of possible $4-$topping pizzas $($from the set of $14$ toppings$)$

$($b$)$ How many bits would you need for the most efficient encoding of a $4-$topping pizza?

$($c$)$ Develop your own encoding$/$decoding algorithm where the code uses this number of bits.

$($d$)$ Use your encoding to encode the following $4-$topping pizzas:

$\{$Pepperoni$,$ Onions, Black Olives, Pesto$\}\{$Anchovies$,$ Green Olives, Mushrooms, Basil$\}$

$($e$)$ Use your decoding to decode the following strings: $($put "non$-$decodable" if you can't decode the string:$)$

$0101010101$

$0011001100$