1. Integer to ASCII string

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1. Integer to ASCII string

• For example, if a0 0000002A, which is
  101010two42ten, then a1 00003234
• addi t0, zero, 10
• div a0, t0 a0/10
• mflo a1 a1 quotient
• addi a1, a1, 0x30 convert to ASCII
• mfhi t0 t0 remainder
• addi t0, t0, 0x30 convert to ASCII
• sll t0, t0, 8
• or a1, a1, t0

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2. Integer Division
See 3.27 solution
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3. MIPS Instruction

• addi a1, zero, 32
• loop addi a1, a1, -4
• lw a0, 8(a1)
• beq a1, zero, exit
• j loop
• exit

70000000 70000004 70000008 7000000C 70000010 70000
014
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4. Floating-Point
(0.3)oct3/8

• 1100 0000 0010 1100 0000 0000 0000 0000
• ?18513-5110.011?64(1/41/8)?24
• Smallest number gt 8-5122-22 gt10-600
• Why no hidden bit?
• For base 2, we can always normalize to 1.M2e.
  For example, (0.1)two (1.0)two2?1, (0.01)two
  (1.0)two2?2, (0.001)two (1.0)two2?3
• For base 8, it is not always possible to
  normalize to 1.M8e. For example,
  (0.1)two(0.1)two80(100.0)two8,
  (0.01)two(0.01)two80(10.0)two8?1
• For any base other than 2, there can not be any
  hidden bit.

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5. Questions

• Booths algorithm
• See 00, 11 do nothing
• See 01, addition
• See 10, subtraction
• Best if 11111111111, 1 add, 1 sub
• Worst if 101010101, 16 add, 16 sub

6

• Speedup
• 2 hours from CLL to AUS
• 4 hours from AUS to LAX, 1200 miles
• Total 6 hours
• Speedup 2, meaning 3 hours
• Alternative answer (assume perm between AUS and
  LAX)
• 1 hour from AUS to LAX gt 1200/hour
• Total 4 hours
• 2 hours from AUS to LAX gt 600/hour

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b) MIPS

• Convert beq a0, 0x1234abcd, exit
• Answer
• lui at, 0x1234
• ori at, at, 0xabcd
• beq a0, at, exit

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e) Floating-Point Associative

• Operation ? is associative if
• a?(b?c) (a?b)?c
• For example, and is associate
• What about division? 3/(4/5)(3/4)/5? No!
• FP addition a(bc)(ab)c?
• 101000(-1010001)0
• (101000-101000)11

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Example Avoid FP error

• To compute the average age for all people in USA
• Method 1
• Add age of all people into total
• Compute total/295,000,000
• Method 2
• Compute average age for each group of 1,000
  people
• Compute the average of every 1,000 groups
• Compute the average of the 295 averages
• Which method produces more accurate result?