Arithmetic ROM Design $($In the notes there is a solved similar problem$)$ Design a digital logic circuit as a Read Only Memory $($ROM$)[$Decoder plus OR gates$].$ A ROM accepts a three$-$bit number and generates an output binary number equal to three times the input number, plus one. $($a$)$ What is the size of the initial $($unsimplified$)$ ROM $?($b$)$ What is the size of the final $($simplified$)$ ROM $?($c$)$ Show in detail the final memory layout.