Teacher answer key

Bits and Representation

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.

22. Bit Masks and Flags

Select individual bits with AND and set them with OR.

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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 13
AND 5
PRINT
OR 2
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 5, 7

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	13	`{"registers":[13,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
AND	1	2	13	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	2	3	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

2. Build and check

Read a byte from 0 through 255. Print only its bits 0 and 2 as a numeric mask, using AND 5.

Required instruction types: INPUT, AND

Example challenge solution

INPUT
AND 5
PRINT
HALT

Actual checker fixtures

Case 1

Input: 7
Initial memory: All bytes initially zero
Expected output: 5

Case 2

Input: 10
Initial memory: All bytes initially zero
Expected output: 0

Case 3

Input: 20
Initial memory: All bytes initially zero
Expected output: 4

Case 4

Input: 255
Initial memory: All bytes initially zero
Expected output: 5

3. Explain the machine

What does the mask5 select?

Reasoning and teaching note

Binary00000101 selects bits 0/2, clearing other bits. It does not numerically subtract other values.

23. Toggling Bits

Use XOR’s reversible change to update a saved setting.

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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 42
XOR 6
PRINT
XOR 6
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 44, 42

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	42	`{"registers":[42,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
XOR	1	2	42	44	`{"registers":[44,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
PRINT	2	3	44	44	`{"registers":[44,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	44

2. Build and check

Read one byte. Toggle bits 1 and 2, store the toggled byte at address 20, and print it after reading it back. Toggle those bits again, save the restored byte at address 20, and print the restored value.

Required instruction types: INPUT, XOR, STORE, LOAD

Example challenge solution

INPUT
XOR 6
STORE 20
LOAD [20]
PRINT
XOR 6
STORE 20
LOAD [20]
PRINT
HALT

Actual checker fixtures

Case 1

Input: 0
Initial memory: All bytes initially zero
Expected output: 6, 0
Expected final memory: 20: 0
Required memory reads: 20

Case 2

Input: 42
Initial memory: All bytes initially zero
Expected output: 44, 42
Expected final memory: 20: 42
Required memory reads: 20

Case 3

Input: 255
Initial memory: All bytes initially zero
Expected output: 249, 255
Expected final memory: 20: 255
Required memory reads: 20

3. Explain the machine

What happens after toggling the same XOR mask twice?

Reasoning and teaching note

Original value returns:42 XOR 6=44, then44 XOR 6=42.

24. Signed Bits and the Largest Value

Understand NOT and test a signed difference with a sign mask.

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 255
NOT
PRINT
NOT
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: -256, 255

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	255	`{"registers":[255,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
NOT	1	2	255	-256	`{"registers":[-256,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":true,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
PRINT	2	3	-256	-256	`{"registers":[-256,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":true,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	-256

2. Build and check

Read two integers, each from −10,000 through 10,000, and print the larger value. Use a subtraction and the signed 32-bit sign mask.

Required instruction types: INPUT, SUB, AND, JUMP_IF_ZERO

Example challenge solution

INPUT
COPY R0 R1
INPUT
COPY R0 R2
LOAD R1
SUB R2
AND -2147483648
JUMP_IF_ZERO first
LOAD R2
JUMP show
first: LOAD R1
show: PRINT
HALT

Actual checker fixtures

Case 1

Input: 5, 9
Initial memory: All bytes initially zero
Expected output: 9

Case 2

Input: 9, 5
Initial memory: All bytes initially zero
Expected output: 9

Case 3

Input: 7, 7
Initial memory: All bytes initially zero
Expected output: 7

Case 4

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

Case 5

Input: -8, -2
Initial memory: All bytes initially zero
Expected output: -2

3. Explain the machine

Why is NOT 255 equal to−256 rather than0?

Reasoning and teaching note

NOT inverts all signed32 bits. A byte-only complement would require a separate mask255.