Blog 3: Math

Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hex 0 1 2 3 4 5 6 7 8 9 A B C D E F

Binary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

1. Convert the following binary numbers to both hexadecimal (base-16) and decimal (base-10)
a. 1011 hexadecimal:B decimal:11
b. 10101 hexadecimal:15 decimal:21
c. 10010110 hexadecimal: 96 decimal:150
d. 1111111 hexadecimal:7F decimal:127

2. Convert the following decimal numbers to both binary (base-2) and hexadecimal (base-16)
a. 8 binary:1000 hexadecimal:8
b. 63 binary:00111111 hexadecimal:3F

c. 113 binary:01110001 hexadecimal:71

d. 97 binary:01100001 hexadecimal:61

3. Suppose that we want to download a 200 MB file. How long will it take on each of the following connections?

a. A modem that can download at 56 kilobits/second

200MB=204800 kilobyte=1638400 kilobits so, 1638400/56=29257.14 seconds, or 8.12 hours
b. A DSL connection that can download at 5 Megabits/second

200MB=1600 Megabits so, 1600/5=320 seconds, or 5.3 minutes
c. A high-speed connection that can download 10 Megabits/second

200MB=1600 Megabits so, 1600/10=160 seconds, or 2.6 minutes.

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? In a month (given a reliable connection)?

1 megabyte is 8 megabits, so 60 megabytes are 480 megabits, the connection can send it in 160 seconds. so in an hour there are 3600 seconds, so 3600/160=22.5 songs in an hour. in a month there are 2629743 seconds in a month so 2 629 743/160=16435.9 songs in a month.