Teacher answer key

Repetition and Counters

Gather four kinds of evidence: prediction of relevant state; behavior across varied cases including boundaries; explanation using trace/state evidence; and a reasoned correction of one mismatch. Mark each as emerging, with support or independent using paper or your school’s existing approved process. A challenge pass is machine-behavior evidence, not proof of authorship or complete mastery. Accept equivalent correct programs; the public key is a model, not the only possible answer.

Public teaching material. Solutions are examples; equivalent correct programs may also pass the actual checks.

13. Loops: Repeating Things

Pair LOOP with RETURN and treat zero repeats correctly.

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1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 8
LOOP 4
  PRINT
RETURN
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 8, 8, 8, 8

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	8	`{"registers":[8,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
LOOP	1	2	8	8	`{"registers":[8,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[{"start":1,"end":3,"remaining":4,"callDepth":0}],"memoryReads":[],"memoryWrites":[]}`	None
PRINT	2	3	8	8	`{"registers":[8,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[{"start":1,"end":3,"remaining":4,"callDepth":0}],"memoryReads":[],"memoryWrites":[]}`	8

2. Build and check

Read a repeat count from 0 through 5. Print 8 exactly that many times, then halt.

Required instruction types: INPUT, LOOP, PRINT, RETURN

Example challenge solution

INPUT
COPY R0 R1
LOAD 8
LOOP R1
PRINT
RETURN
HALT

Actual checker fixtures

Case 1

Input: 0
Initial memory: All bytes initially zero
Expected output: None

Case 2

Input: 1
Initial memory: All bytes initially zero
Expected output: 8

Case 3

Input: 4
Initial memory: All bytes initially zero
Expected output: 8, 8, 8, 8

3. Explain the machine

How many times does LOOP 0 execute its body?

Reasoning and teaching note

Zero; it skips the paired body/RETURN. A negative count errors instead.

14. Building a Counter

Print 1 to 10 and generalize the count.

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1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 5
again: PRINT
SUB 1
JUMP_IF_ZERO done
JUMP again
done: HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 5, 4, 3, 2, 1

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	5	`{"registers":[5,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
PRINT	1	2	5	5	`{"registers":[5,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	5
SUB	2	3	5	4	`{"registers":[4,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	5

2. Build and check

Read N from 0 through 10 and print every integer from 1 through N in order. For N = 0, print nothing.

Required instruction types: INPUT, LOOP, ADD, PRINT

Example challenge solution

INPUT
COPY R0 R2
LOAD 1 R1
LOOP R2
LOAD R1
PRINT
ADD 1
COPY R0 R1
RETURN
HALT

Actual checker fixtures

Case 1

Input: 0
Initial memory: All bytes initially zero
Expected output: None

Case 2

Input: 3
Initial memory: All bytes initially zero
Expected output: 1, 2, 3

Case 3

Input: 10
Initial memory: All bytes initially zero
Expected output: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

3. Explain the machine

How do counter value and number of repetitions differ?

Reasoning and teaching note

Counter is changing state; LOOP count is captured at entry. Correct start/increment/order makes1..N with no output for0.

15. Sum One to N

Keep an accumulator separate from the loop counter.

Open this lesson →

1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 1 R1
LOAD 0 R2
LOOP 4
LOAD R2
ADD R1
COPY R0 R2
LOAD R1
ADD 1
COPY R0 R1
RETURN
LOAD R2
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 10

Instruction	PC before	PC after	Relevant state	Output
LOAD	0	1	`{"registers":[0,1,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
LOAD	1	2	`{"registers":[0,1,0,0,0,0,0,0],"flags":{"zero":true,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
LOOP	2	3	`{"registers":[0,1,0,0,0,0,0,0],"flags":{"zero":true,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[{"start":2,"end":9,"remaining":4,"callDepth":0}],"memoryReads":[],"memoryWrites":[]}`	None

2. Build and check

Read N from 0 through 10. Use a loop to print the sum 1 + 2 + … + N. Print 0 for N = 0.

Required instruction types: INPUT, LOOP, ADD

Example challenge solution

INPUT
COPY R0 R3
LOAD 1 R1
LOAD 0 R2
LOOP R3
LOAD R2
ADD R1
COPY R0 R2
LOAD R1
ADD 1
COPY R0 R1
RETURN
LOAD R2
PRINT
HALT

Actual checker fixtures

Case 1

Input: 0
Initial memory: All bytes initially zero
Expected output: 0

Case 2

Input: 4
Initial memory: All bytes initially zero
Expected output: 10

Case 3

Input: 10
Initial memory: All bytes initially zero
Expected output: 55

3. Explain the machine

What does the total represent after k iterations?

Reasoning and teaching note

1+…+k; initially0. N=0 leaves total 0.