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Solutions
1

Chapter 1 Solutions S-3
1.1 Personal computer (includes workstation and laptop): Personal computers
emphasize delivery of good performance to single users at low cost and usually
execute third-party so ware.
Personal mobile device (PMD, includes tablets): PMDs are battery operated
with wireless connectivity to the Internet and typically cost hundreds of
dollars, and, like PCs, users can download so ware (“apps”) to run on them.
Unlike PCs, they no longer have a keyboard and mouse, and are more likely
to rely on a touch-sensitive screen or even speech input.
Server: Computer used to run large problems and usually accessed via a network.
Warehouse scale computer: ousands of processors forming a large cluster.
Supercomputer: Computer composed of hundreds to thousands of processors
and terabytes of memory.
Embedded computer: Computer designed to run one application or one set
of related applications and integrated into a single system.
1.2
a. Performance via Pipelining
b. Dependability via Redundancy
c. Performance via Prediction
d. Make the Common Case Fast
e. Hierarchy of Memories
f. Performance via Parallelism
g. Design for Moore’s Law
h. Use Abstraction to Simplify Design
1.3 e program is compiled into an assembly language program, which is then
assembled into a machine language program.
1.4
a. 1280 ⫻ 1024 pixels ⫽ 1,310,720 pixels ⫽⬎ 1,310,720 ⫻ 3 ⫽ 3,932,160
bytes/frame.
b. 3,932,160 bytes ⫻ (8 bits/byte) /100E6 bits/second ⫽ 0.31 seconds
1.5
a. performance of P1 (instructions/sec) ⫽ 3 ⫻ 10
9
/1.5 ⫽ 2 ⫻ 10
9
performance of P2 (instructions/sec) ⫽ 2.5 ⫻ 10
9
/1.0 ⫽ 2.5 ⫻ 10
9
performance of P3 (instructions/sec) ⫽ 4 ⫻ 10
9
/2.2 ⫽ 1.8 ⫻ 10
9

S-4 Chapter 1 Solutions
b. cycles(P1) ⫽ 10 ⫻ 3 ⫻ 10
9
⫽ 30 ⫻ 10
9
s
cycles(P2) ⫽ 10 ⫻ 2.5 ⫻ 10
9
⫽ 25 ⫻ 10
9
s
cycles(P3) ⫽ 10 ⫻ 4 ⫻ 10
9
⫽ 40 ⫻ 10
9
s
c. No. instructions(P1) ⫽ 30 ⫻ 10
9
/1.5 ⫽ 20 ⫻ 10
9
No. instructions(P2) ⫽ 25 ⫻ 10
9
/1 ⫽ 25 ⫻ 10
9
No. instructions(P3) ⫽ 40 ⫻ 10
9
/2.2 ⫽ 18.18 ⫻ 10
9
CPI
new
⫽ CPI
old
⫻ 1.2, then CPI(P1) ⫽ 1.8, CPI(P2) ⫽ 1.2, CPI(P3) ⫽ 2.6
f ⫽ No. instr. ⫻ CPI/time, then
f(P1) ⫽ 20 ⫻ 10
9
⫻1.8/7 ⫽ 5.14 GHz
f(P2) ⫽ 25 ⫻ 10
9
⫻ 1.2/7 ⫽ 4.28 GHz
f(P1) ⫽ 18.18 ⫻ 10
9
⫻ 2.6/7 ⫽ 6.75 GHz
1.6
a. Class A: 10
5
instr. Class B: 2 ⫻ 10
5
instr. Class C: 5 ⫻ 10
5
instr.
Class D: 2 ⫻ 10
5
instr.
Time ⫽ No. instr. ⫻ CPI/clock rate
Total time P1 ⫽ (10
5
⫹ 2 ⫻ 10
5
⫻ 2 ⫹ 5 ⫻ 10
5
⫻ 3 ⫹ 2 ⫻ 10
5
⫻ 3)/(2.5 ⫻
10
9
) ⫽ 10.4 ⫻ 10
⫺4
s
Total time P2 ⫽ (10
5
⫻ 2 ⫹ 2 ⫻ 10
5
⫻ 2 ⫹ 5 ⫻ 10
5
⫻ 2 ⫹ 2 ⫻ 10
5
⫻ 2)/
(3 ⫻ 10
9
) ⫽ 6.66 ⫻ 10
⫺4
s
CPI(P1) ⫽ 10.4 ⫻ 10
⫺4
⫻ 2.5 ⫻ 10
9
/10
6
⫽ 2.6
CPI(P2) ⫽ 6.66 ⫻ 10
⫺4
⫻ 3 ⫻ 10
9
/10
6
⫽ 2.0
b. clock cycles(P1) ⫽ 10
5
⫻ 1⫹ 2 ⫻ 10
5
⫻ 2 ⫹ 5 ⫻ 10
5
⫻ 3 ⫹ 2 ⫻ 10
5
⫻ 3
⫽ 26 ⫻ 10
5
clock cycles(P2) ⫽ 10
5
⫻ 2⫹ 2 ⫻ 10
5
⫻ 2 ⫹ 5 ⫻ 10
5
⫻ 2 ⫹ 2 ⫻ 10
5
⫻ 2
⫽ 20 ⫻ 10
5
1.7
a. CPI ⫽ T
exec
⫻ f/No. instr.
Compiler A CPI ⫽ 1.1
Compiler B CPI ⫽ 1.25
b. f
B
/f
A
⫽ (No. instr.(B) ⫻ CPI(B))/(No. instr.(A) ⫻ CPI(A)) ⫽ 1.37
c. T
A
/T
new
⫽ 1.67
T
B
/T
new
⫽ 2.27

Chapter 1 Solutions S-5
1.8
1.8.1 C ⫽ 2 ⫻ DP/(V
2
*F)
Pentium 4: C ⫽ 3.2E–8F
Core i5 Ivy Bridge: C ⫽ 2.9E–8F
1.8.2 Pentium 4: 10/100 ⫽ 10%
Core i5 Ivy Bridge: 30/70 ⫽ 42.9%
1.8.3 (S
new
⫹ D
new
)/(S
old
⫹ D
old
) ⫽ 0.90
D
new
⫽ C ⫻ V
new
2 ⫻ F
S
old
⫽ V
old
⫻ I
S
new
⫽ V
new
⫻ I
erefore:
V
new
⫽ [D
new
/(C ⫻ F)]
1/2
D
new
⫽ 0.90 ⫻ (S
old
⫹ D
old
) ⫺ S
new
S
new
⫽ V
new
⫻ (S
old
/V
old
)
Pentium 4:
S
new
⫽ V
new
⫻ (10/1.25) ⫽ V
new
⫻ 8
D
new
⫽ 0.90 ⫻ 100 ⫺ V
new
⫻ 8 ⫽ 90 ⫺ V
new
⫻ 8
V
new
⫽ [(90 ⫺ V
new
⫻ 8)/(3.2E8 ⫻ 3.6E9)]
1/2
V
new
⫽ 0.85 V
Core i5:
S
new
⫽ V
new
⫻ (30/0.9) ⫽ V
new
⫻ 33.3
D
new
⫽ 0.90 ⫻ 70 ⫺ V
new
⫻ 33.3 ⫽ 63 ⫺ V
new
⫻ 33.3
V
new
⫽ [(63 ⫺ V
new
⫻ 33.3)/(2.9E8 ⫻ 3.4E9)]
1/2
V
new
⫽ 0.64 V
1.9
1.9.1
p # arith inst. # L/S inst. # branch inst. cycles ex. time speedup
1 2.56E9 1.28E9 2.56E8 7.94E10 39.7 1
2 1.83E9 9.14E8 2.56E8 5.67E10 28.3 1.4
4 9.12E8 4.57E8 2.56E8 2.83E10 14.2 2.8
8 4.57E8 2.29E8 2.56E8 1.42E10 7.10 5.6

S-6 Chapter 1 Solutions
1.9.2
p ex. time
1 41.0
2 29.3
4 14.6
8 7.33
1.9.3 3
1.10
1.10.1 die area
15cm
⫽ wafer area/dies per wafer ⫽ pi*7.5
2
/ 84 ⫽ 2.10 cm
2
yield
15cm
⫽ 1/(1⫹(0.020*2.10/2))
2
⫽ 0.9593
die area
20cm
⫽ wafer area/dies per wafer ⫽ pi*10
2
/100 ⫽ 3.14 cm
2
yield
20cm
⫽ 1/(1⫹(0.031*3.14/2))
2
⫽ 0.9093
1.10.2 cost/die
15cm
⫽ 12/(84*0.9593) ⫽ 0.1489
cost/die
20cm
⫽ 15/(100*0.9093) ⫽ 0.1650
1.10.3 die area
15cm
⫽ wafer area/dies per wafer ⫽ pi*7.5
2
/(84*1.1) ⫽ 1.91 cm
2
yield
15cm
⫽ 1/(1 ⫹ (0.020*1.15*1.91/2))
2
⫽ 0.9575
die area
20cm
⫽ wafer area/dies per wafer ⫽ pi*10
2
/(100*1.1) ⫽ 2.86 cm
2
yield
20cm
⫽ 1/(1 ⫹ (0.03*1.15*2.86/2))
2
⫽ 0.9082
1.10.4 defects per area
0.92
⫽ (1–y^.5)/(y^.5*die_area/2) ⫽ (1⫺0.92^.5)/
(0.92^.5*2/2) ⫽ 0.043 defects/cm
2
defects per area
0.95
⫽ (1–y^.5)/(y^.5*die_area/2) ⫽ (1⫺0.95^.5)/
(0.95^.5*2/2) ⫽ 0.026 defects/cm
2
1.11
1.11.1 CPI ⫽ clock rate ⫻ CPU time/instr. count
clock rate ⫽ 1/cycle time ⫽ 3 GHz
CPI(bzip2) ⫽ 3 ⫻ 10
9
⫻ 750/(2389 ⫻ 10
9
)⫽ 0.94
1.11.2 SPEC ratio ⫽ ref. time/execution time
SPEC ratio(bzip2) ⫽ 9650/750 ⫽ 12.86
1.11.3. CPU time ⫽ No. instr. ⫻ CPI/clock rate
If CPI and clock rate do not change, the CPU time increase is equal to the
increase in the of number of instructions, that is 10%.
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