design the hardware to implement the following function:

E $=$ A $/2^$i $+$ B $*2^$j

F $=$ E $*$ C

without using $<<,>>,*,/,+,-$ and ue a full adder Where:

$$ A$,$ B$,$ C and E are $8-$bit unsigned numbers

$$ i and j are $3-$bit unsigned numbers.

$$ F is $16-$bit unsigned number