1. 1. Integer to ASCII string
For example, if $a0 = A, which is two=42ten, then $a1 =
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. 2. Integer Division
See 3.27 solution

3. 3. MIPS Instruction addi $a1, $zero, 32 loop: addi $a1, $a1, -4
lw $a0, 8($a1)
beq $a1, $zero, exit
j loop
exit C
001000
00000
00101
100011
00100
000100
000010

4. 4. Floating-Point (0.3)oct=3/8 1100 0000 0010 1100 0000 0000 0000 0000
1* *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. 5. Questions Booths algorithm: See 00, 11 do nothing See 01, addition
See 10, subtraction
Best if …, 1 add, 1 sub
Worst if …, 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 => 1200/hour
Total 4 hours
2 hours from AUS to LAX => 600/hour

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

8. 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)+1=1

9. 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?