1. Integer to ASCII string

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Presentation transcript:

1. Integer to ASCII string For example, if $a0 = 0000002A, which is 101010two=42ten, 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

2. Integer Division See 3.27 solution

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 70000014 001000 00000 00101 0000 0000 0010 0000 1111 1111 1111 1100 100011 00100 0000 0000 0000 1000 000100 0000 0000 0000 0001 000010 0000 0000 0000 0000 0000 0000 01

4. Floating-Point (0.3)oct=3/8 1100 0000 0010 1100 0000 0000 0000 0000 1*8513-511*0.011=64*(1/4+1/8)=24 Smallest number > 8-512*2-22 >10-600 Why no hidden bit? For base 2, we can always normalize to 1.M*2e. For example, (0.1)two = (1.0)two*21, (0.01)two= (1.0)two*22, (0.001)two = (1.0)two*23 For base 8, it is not always possible to normalize to 1.M*8e. For example, (0.1)two=(0.1)two*80=(100.0)two*8, (0.01)two=(0.01)two*80=(10.0)two*81 For any base other than 2, there can not be any hidden bit.

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

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 => 1200/hour Total 4 hours 2 hours from AUS to LAX => 600/hour

b) MIPS Convert beq $a0, 0x1234abcd, exit Answer: lui $at, 0x1234 ori $at, $at, 0xabcd beq $a0, $at, exit

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+(b+c)=(a+b)+c? 10^1000+(-10^1000+1)=0 (10^1000-10^1000)+1=1

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?