Python Output

1)
a. 12
b. 42
c. 0
d. it adds a to itself b times

2)
a. 5
b. 4
c. 7
d. it divides a by b

3)
a. strange: a = 6
b. weird: a = 8 b = 4
strange: a = 12
c. strange: a = 4
reallyWeird: a = 8 b = 4
strange: a = 12
d. downrightOdd: a = 3
strange: a = 3
reallyWeird: a = 6 b = 3
strange: a = 9

4)
a. 1
b. 3

Math

1. Convert the following binary numbers to both hexadecimal (base-16) and decimal (base-10)

So in starting to try to figure out how to solve these problems I have come to the conclusion that these numbers which I am going to convert to the hexadecimal (base-16) and decimal (base-10) are currently base-2. This is because base-2 only uses the digits 0 and 1. Base-2 is what computers use. Each base-2 digit is a bit. There are 4 bits for each hexadecimal.

a. 1011

for base-16:

the numbers you refer to are 8, 4, 2, 1
so there is one 8. one 2. one 1.
1 * 16^3 + 0 * 16^2 + 1 * 16^1 + 1 * 16^0
=
8+2+1=
11=B with a base of 16

for base-10:

the numbers you refer to are 8, 4, 2, 1

so there is one 8. one 2. one 1.

1 * 10^3 + 0 * 10^2 + 1 * 10^1 + 1 * 10^0

=

8+2+1=

11 with a base of 10

b. 10101

for base-16:
there are more than 4 1 and 0 digits so it needs to be broken up into pairs of 4
0001 0101
the numbers you refer to are 128, 64, 32, 16, 8, 4, 2, 1
there is one 16. one 4. one 1.
0 * 16^7 + 0 * 16^6 + 0 * 16^5 + 1 * 16^4 + 0 * 16^3 + 1 * 16^2 + 0 * 16^1 + 1 * 16^0
=
16+4+1=
21=6F with a base of 16

for base-10:

the numbers you refer to are 16, 8, 4, 2, 1

there is one 16. one 4. one 1.

1 * 10^4 + 0 * 10^3 + 1 * 10^2 + 0 * 10^1 + 1* 10^0

=

16+4+1=

21 with a base of 10

c. 10010110

for base-16:

again, it needs to be broken up into 4s
1001 0110
the numbers you refer to are 128, 64, 32, 16, 8, 4, 2, 1
there is one 128. one 16. one 4. one 2.
1 * 16^7 + 0 * 16^6 + 0 * 16^5 + 1 * 16^4 + 0 * 16^3 + 1 * 16^2 + 1 * 16^1 + 0 * 16^0
=
128+16+4+2=
150=FFFFFFFFFF with a base of 16

for base-10:

the numbers you refer to are 128, 64, 32, 16, 8, 4, 2, 1

there is one 128. one 16. one 4. one 2.

1 * 10^7 + 0 * 10^6 + 0 * 10^5 + 1 * 10^4 + 0 * 10^3 + 1 * 10^2 + 1 * 10^1 + 0 * 10^0

=

128+16+4+2=

150 with a base of 10

d. 1111111

for base-16:

broken up into 4s
0111 1111
the numbers you refer to are 128, 64, 32, 16, 8, 4, 2, 1
there is one 64. one 32. one 16. one 8. one 4. one 2. one 1.
0 * 16^7 + 1 * 16^6 + 1 * 16^5 + 1 * 16^4 + 1 * 16^3 + 1 * 16^2 + 1 * 16^1 + 1 * 16^0
=
64+32+16+8+4+2+1=
127=7FFFFFFFF with a base of 16

for base-10:

the numbers you refer to are 64, 32, 16, 8, 4, 2, 1

there is one 64. one 32. one 16. one 8. one 4. one 2. one 1.

1 * 10^6 + 1 * 10^5 + 1 * 10^4 + 1 * 10^3 + 1 * 10^2 + 1 * 10^ 1 + 1 * 10^0

=

64+32+16+8+4+2+1=

127 with a base of 10

2. Convert the following decimal numbers to both binary (base-2) and hexadecimal (base-16)

a. 8

for base-2:

the numbers you refer to are 8, 4, 2, 1

there is one 8.

1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0

=

1000

for base-16:

because the letters are only used for numbers 10-15, there are no letters or changes
simply=8 with a base of 16

b. 63

for base-2:

the numbers you refer to are 32, 16, 8, 4, 2, 1

there is one 32. one 16. one 8. one 4. one 2. one 1.

1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0

=

32+16+8+4+2+1=

111111

for base-16:

only conversion is to add letters
F stands for 15
15 goes into 63 4 times with a remainder of 3
the hexadecimal of 63 = 3FFFF with a base of 16

c. 113

for base-2:

the numbers you refer to are 64, 32, 16, 8, 4, 2, 1

there is one 64. one 32. one 16. one 1.

1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0

=

64+32+16+1=

1110001

for base-16:
F stands for 15
15 goes into 113 7 times with a remainder of 8
the hexadecimal of 113 = 8FFFFFFF with a base of 16

d. 97

for base-2:

the numbers you refer to are 64, 32, 16, 8, 4, 2, 1

there is one 64. one 32. one 1.

1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0

=

64+32+1=

1100001

for base-16:
F stands for 15
15 goes into 97 6 times with a remainder of 7
the hexadecimal of 97 = 7FFFFFF with a base of 16

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

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

For every 1 megabyte there are 1024 kilobytes

200 * 1024 = 204.800 kilobytes

The time it takes to download is in kilobits, so the kilobytes need to be converted to kilobits by mutliplying by 8

204.800 * 8 = 1,638.400 kilobits

Then to find the exact time the modem will take to download, the total number of kilobits the file is needs to be divided by the number of kilobits that download per second

1,638.400 / 56 = 29.2571429
So it will take the modem 29.2571429 seconds to download the 200 megabyte file

b. A DSL connection that can download at 5 Megabits/second

The 200 MB (which I believe stands for megabytes) file needs to be converted into megabits For Every 1 megabyte there are 8 megabits
200 * 8 = 1600 megabits
For every 200 megabytes there are 1600 megabits
The total number of megabits the file is (1600) needs to be divided by the amount of megabits the DSL can download per second (5)
1600 / 5 = 320
So it will take the DSL 320 seconds to download the 200 megabyte file

c. A high-speed connection that can download 10 Megabits/second

The 200 MB file needs to be converted into megabits, because that is how this high-speed connection translates its downloads
For every 1 megabyte there are 8 megabits
200 * 8 = 1600
For every 200 megabytes there are 1600 megabits
Now the number of megabits the file is (1600) simply needs to be divided by the amount of megabits that the high speed connection can download per second (10)
1600 / 10 = 160
It will take the high speed connection 160 seconds to download the 200 megabyte file

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)?

Since the MP3 is in megabytes and the Internet connection uploads with megabits, the MP3 needs to be converted into megabits
For every 1 megabyte there are 8 megabits
60 * 8 = 480
For every 60 megabytes there are 480 megabits
To find the amount of time it takes the Internet to upload one MP3, divide the number of megabits 1 MP3 is (480) by the number of megabits the Internet can upload per second (3)
480 / 3 = 160
It takes the Internet 160 seconds or 2 minutes and 40 seconds to upload 1 MP3
To find how many MP3s can upload in an hour:
Find the total seconds in an hour, there are 60 seconds in 1 minute, and 60 minutes in 1 hour
60 * 60 = 3600 seconds in an hour
With the Internet uploading 1 MP3 in 160 seconds, the total number of seconds in an hour (3600) needs to be divided by the amount of time each MP3 takes to upload (160)
3600 / 160 = 22.5
The Internet can upload 22 and half, really 22 MP3s every hour
To find how many MP3s can upload in a month:
Basing the month off one consisting of 28 days, there are 672 hours in that month
Since the Internet uploads 22 MP3s in 1 hour, the number of hours in a month (672) needs to be multiplied by the number of MP3s uploaded in 1 hour (22)
672 * 22 = 14,784
The Internet can upload 14,784 MP3s in a month (given a reliable connection)