a$)$ We would like to understand how the choice of doubling time in Moore$$s Law affects the increase in the number of transistors that fit on a fixed$-$size chip. We have discussed the fact that the book quotes the doubling time as $18$ months whereas it is commonly quoted as $2$ years. Assume that at year $0,$ T transistors fit on a chip with area A$.$ Calculate the number of transistors

on a chip of size $5$A for year $0$ and then every three years for the next $15$ years, first using a two$-$

year doubling time and then using $18$ months. Print out the associated semi$-$logarithmic graph sheet $($or draw and label on your answer sheet$),$ mark the points on the graph and draw the curves$/$lines that represent the ideal relationship between time and number of transistors on the chip of size $5$A$.$ Draw the graphs for the two$-$year and $18-$month relationships on the same sheet and clearly label them.

b$)$ Assuming that the shape of a transistor is square, find the ratio of one side of the transistor at the end of $15$ years to that at year $0.$ Calculate separately for a doubling time of two years and $18$ months.