The document traces the step-by-step process of calculating the factorial of 3 using a recursive algorithm on a simple CPU. It initializes registers and memory locations, pushes parameters onto the stack, recursively calls the factorial function, and pops values off the stack until it reaches the base case and returns the result.

1. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

2. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
r1 3
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

3. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
r1 3
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

4. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
CPU Registers Memory
???
r1
r13
r14
100
101
102
103
104
105
r15 100
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

5. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

6. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

7. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

8. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

9. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100,101
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

10. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
100
101
102
103
104
105
r15 100,101
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

11. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
3
100
101
102
103
104
105
r15 100,101
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

12. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
3
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
r15
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

13. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
3
03
r1
r13
r14
CPU Registers Memory
3
03
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

14. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3, 2
03
r1
r13
r14
3
03
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

15. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03
r1
r13
r14
3
03
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

16. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

17. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

18. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
100
101
102
103
104
105
r15 100,101,102
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

19. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
100
101
102
103
104
105
r15 100,101,102,103
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

20. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
2
100
101
102
103
104
105
r15 100,101,102,103
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

21. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
2
100
101
102
103
104
105
100,101,102,103,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

22. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2
03,15
r1
r13
r14
3
03
2
15
100
101
102
103
104
105
100,101,102,103,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

23. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15
r1
r13
r14
3
03
2
15
100
101
102
103
104
105
100,101,102,103,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

24. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15,15
r1
r13
r14
3
03
2
15
100
101
102
103
104
105
100,101,102,103,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

25. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15,15
r1
r13
r14
3
03
2
15
100
101
102
103
104
105
100,101,102,103,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

26. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15,15
r1
r13
r14
3
03
2
15
100
101
102
103
104
105
100,101,102,103,
104,105
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

27. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

28. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

29. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1
03,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

30. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
03,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

31. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
03,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

32. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
03,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

33. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
1
03,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

34. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
1
03,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

35. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
1
03,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

36. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
1
03,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

37. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
1
03,15,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

38. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0
1
03,15,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

39. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1
1
03,15,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

40. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1
1
03,15,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

41. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1
1,1
03,15,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

42. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1
1,1
03,15,15,15,15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

43. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1
1,1
03,15,15,15,15,
15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

44. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1
1,1
03,15,15,15,15,
15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

45. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2
1,1
03,15,15,15,15,
15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

46. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2
1,1
03,15,15,15,15,
15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

47. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2
1,1,2
03,15,15,15,15,
15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

48. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2
1,1,2
03,15,15,15,15,
15
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

49. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2
1,1,2
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

50. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2
1,1,2
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

51. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2,3
1,1,2
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

52. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2,3
1,1,2
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101,
100
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

53. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2,3
1,1,2,6
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101,
100
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

54. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2,3
1,1,2,6
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101,
100
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

55. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2,3
1,1,2,6
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101,
100
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4

56. main
factorial
store
to stack
recursive case
load
from stack
base
case
Trace what happens for an input of 3...
CPU Registers Memory
3,2,1,0,1,2,3
1,1,2,6
03,15,15,15,15,
15,03
r1
r13
r14
3
03
2
15
1
100
101
102
103
104
105
100,101,102,103,
104,105,106,105,
104,103,102,101,
100
r15
"the stack"
input: x
return value (the "result")
return address (line #)
the stack pointer
00 read r1
01 setn r15 100
02 call r14 06
03 write r13
04 halt
05 nop
06 jnez r1 09
07 setn r13 1
08 jumpr r14
09 addn r15 1
10 storer r1 r15
11 addn r15 1
12 storer r14 r15
13 addn r1 -1
14 call r14 06
15 loadr r14 r15
16 addn r15 -1
17 loadr r1 r15
18 addn r15 -1
19 mul r13 r13 r1
20 jumpr r14
106
107
It's easy to get lost!
15
Follow the line numbers below to stay on track...
r15
0, 1, 2, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 9, 10, 11, 12, 13, 14, 6, 7, 8 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 3, 4