$8.$ One challenge for architects is that the design created today will require several years of

implementation, verification, and testing before appearing on the market. This means that the

architect must project what the technology will be like several years in advance. Sometimes, this

is difficult to do$.$

a$.$ According to the trend in device scaling historically observed by Moore$$s Law, the number of

transistors on a chip in $2025$ should be how many times the number in $2015?[$assume # Transistors

double every $2$ years$]$

b$.$ The increase in performance once mirrored this trend. Had performance continued to climb at

the same rate as in the $1990$s$,$ approximately what performance would chips have over the VAX$11/780$ in $2025?[$assume performance increases $52\%$ every year$]$

c$.$ What has limited the rate of growth of the clock rate, and what are architects doing with the

extra transistors now to increase performance?