1) Convert the following numbers from base 2 to base 10.
1. 1011= (2^3) + (2^1) + (2^0) = 10 + 11= 21
2. 101010= (2^5) + (2^3) + (2^1)= 32 + 8 + 2= 42
3. 11111= (2^4) + (2^3) + (2^2) + (2^1) = 31
4. 10010= (2^4) + (2^1) = 16 + 2 = 18
2) Convert the following numbers from base 10 to base 2.
1. 31= (2^4)+(2^3)+(2^2)+(2^1)+(2^0)= 11111
2. 51= (2^5)+(2^4)+(2^1)+(2^0)= 110011
3. 7= (2^2)+(2^1)+(2^0)= 111
4. 103= (2^6)+(2^5)+(2^2)+(2^1)+(2^0)= 1100111
3) Suppose that we want to download a 100 MB file. How long will it take on each of the following connections?
1. 56 Kilobits/sec
(56 kilobits/sec)/(8)= 7 kilobytes/sec
7 kilobytes/sec=0.007 megabytes/sec
(1s/0.007MB)= 142 sec/MB
(142 sec/MB)x(100)= (14200sec)/60=236.67min.
237/60=3.95=~4hours
2. 5 Megabits
(5MB/sec)/8=0.625MB/sec
(1sec/0.625MB)=1.6s/MB
(1.6 s/MB) x (100)= (160 sec.)/60= 2min. 40 Sec.
3. 10 Megabits/sec
(10 MB/sec)/(8)= 1.25 MB/sec
(1 sec/ 1.25MB)= .8s/MB
(.8 sec/MB)x(100)= 80 sec.
1 min 20 sec
4) If we have an Internet connection that can upload 3 Megabits/second, and an MP3 is 60 Megabytes, how many MP3s can we upload in an hour?
3mb/sec=.375 Megabytes/sec
1 sec/ .375 MB= 2.66 sec/MB
(2.66 sec/MB) x (60)= 160 sec= 2.66 min
60 min/2.66= 22.5= 22MP3/hr.
