15-347 Spring '98, Exam 1  Official solution 

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PROBLEM 1.

MAX ERROR = 5/(10000 - 5) ~= 5E-4

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PROBLEM 2.

[There were some problems in the design of this problem.  The results
 were less "interesting" than had been intended.]

A.
	Bits	n=1	n=2
	000	0	0
	001	1/2	1/2
	010	1	1
	011	3/2	3/2
	100	inf	2
	101	nan	3
	110	nan	inf
	111	nan	nan

B.
	Value	n=1	n=2
	1/8	0	0
	1/3	1/2	1/2
	1/4	0	0
	1	1	1
	4	inf	inf

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PROBLEM 3.

A.	12 tag, 2 index, 2 offset bits
B.	
	Referencing any of the following byte addresses could
	cause the block containing address 0x0103 to be overwritten
	0x0110 .. 0x0113
	0x0120 .. 0x0123
	0x0130 .. 0x0133
	0x0140 .. 0x0143
   

C.
	Addresses 0x0121, 0x0125, 0x0129, 0x012D
D.
	Addresses 0x0140, 0x0144, 0x0148, 0x014C
E.
	75% [Misses 1st byte in each block, hits rest]

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PROBLEM 4.

A. 128
B. 128 * 3 * 19 = 7296
C. 128 * 3 * 2 =  768
D. 128 * 3     = 384
E. 7296 + 768 + 384 + 96*1024*8 = 794,880
F. Must be a data cache, since it has a dirty bit [Icache is read-only]

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PROBLEM 5.

Must send 30 * 1024 * 1024 = 30 Megapixels/second over bus with
80 Mbit/second capacity.  Can have 8/3 bits per pixel.  Round this down
to 2 bits per pixel, allowing 4 gray scale levels.

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PROBLEM 6.

A.

	4KB = 8 sectors = 2/5 revolutions

	Disk requires 10ms to make full revolution

	Maximum Transfer time =
           10ms seek + 10ms rot. latency = 2/5 * 10 transfer = 24 ms

B.

	Speeding disk by k would give transfer time 10 + 14/k 
	Must have k=7 to get 12.
	Disk must run at 6000 * 7 = 42000 RPM

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PROBLEM 7.

Part 1: 
  1 7FFFFFFF
  2 FFFFFFFF
  3 00080000
  4 00080000

Part 2:
  1 F 	e.g.,  ux = 0
  2 T   [Must have MSB = 1]
  3 F 	e.g., x = Tmin, y = 1 or Tmax
  4 T   [ux must have MSB = 1, and ux != TMin]
  5 T   [Low order bits of product identical for unsigned & signed]
  6 F 	e.g., x = y = Tmax   

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