A $1$M$-$byte memory system is to be constructed using $256K$ by $4$ RAM chips.

$($i$)$ How many chips are required for this memory system?

$($ii$)$ If the address of the first memory location is $0,$ what is the address of the last one in decimal and hexadecimal?

$($iii$)$ How many bits are required for the address decoder?

$($iv$)$ Draw the interconnection of the RAM chips, the source and receiver, and the address decoder. Clearly indicate the number of bits used in the address and data bus.