Consider a paging system. The logical address space has $6$ pages of $128$ words each, mapped onto a physical memory of $256$ frames. $(4$ points$)$

a$)$ How many bits are there in the logical address?

b$)$ How many bits are there in the physical address?

c$)$ What is the logical address of the last word in page $2?$

d$)$ What is the physical address of the third word in the $5^{th}$ frame?