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CIS 3360 – Security in Computing
Spring 2010
Solution for Homework 5 (100 points)
1)
[5]
Fill the following table:
1 THz
=
____10
12
____ Hz
1 GHz
=
____10
9
_____
Hz
1 MHz
=
____10
6
_____ Hz
1 KHz
=
____10
3
_____ Hz
1 Hz
=
_____1____
cycles per second
2)
[5]
If a frequency is given as 1 MHz, how much time in milliseconds does one cycle
take? Recall that 1 milliseconds = 1ms = 10
3
seconds.
Answer:
Frequency
=
Cycle / Second
1 MHz
=
1000000/1000
cycles/ms
=
1000 cycles/ms
Thus 1 cycle takes 1/1000 ms = 0.001 ms
3)
[10]
If a data block has 512 bytes and the bus is 32 bit wide, how much time in
microseconds does it take to fetch the entire data block assuming the bus operates at 1
MHz? If the bus is 64 bits wide, running at 1 MHz, how much time (in
μ
s) does it
take? If the bus is 32bits wide, running at 4 MHz, how much time (in
μ
s) does it
take? Recall that 1 microseconds = 1
μ
s = 10
6
seconds.
Answer:
Case 1: 32bit wide bus, running at 1 MHz
First, we will find the no. of cycles it takes to transfer the 512 bytes on a 32bit wide bus
# of cycles
= (512 bytes * 8 bits) / 32 bits
= 4096 bits / 32 bits
= 128 cycles
Now, we will find the time for one cycle:
The bus is running at 1 MHz. So, 1 cycle will take 1/1000 000 secs = 10
6
s = 1
μ
s.
So, time for 128 cycles is: 128 x 1
μ
s = 128
μ
s
Thus, it takes 128 microseconds to transfer entire block.
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Case 2: 64bit wide bus, running at 1 MHz
# of cycles
= (512 bytes * 8 bits) / 64 bits
= 4096 bits / 64 bits
=
64 cycles
The bus operates 1000000 cycles in 1 second.
Thus, the operation of 64 cycles, it should take (64/1000000) = 0.000064 second.
1 second
=
10
6
microseconds
0.000064 second
= 0.000064 x 10
6
= 64 microseconds
Thus, it takes 64 microseconds to transfer entire block.
Case 3: 32bit wide bus, running at 4 MHz
# of cycles
= (512 bytes * 8 bits) / 32 bits
= 4096 bits / 32 bits
= 128 transfers
The bus operates 4000000 cycles in 1 second.
Thus, the operation of 128 cycles, it should take (128/4000000) = 0.000032
second.
1 second
=
10
6
microseconds
0.000032 second
= 0.000032 x 10
6
= 32 microseconds
Thus, it takes 32 microseconds to transfer entire block.
4)
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 Spring '10
 Guha
 Hertz, Power of two, physical address space

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