📚 OpenKernel EDU3D3D

← All teacher resources

Teaching the visible machine

Bits and Representation

Select and toggle bits and explain signed 32-bit behavior.

Total classroom time: 135 minutes · 3 × 45 minutes

Learning outcomes

  • Apply AND masks to select bits.
  • Use OR to set bits.
  • Demonstrate XOR involution.
  • Distinguish signed32-bit NOT from byte inversion and constrain sign-mask comparison to its documented small range.

Before class

give an eight-column binary place-value table and a signed32-bit sign-bit note. Use masks5=00000101 and6=00000110. Explain that bit operations coerce to signed32 bits, while register arithmetic does not wrap.

Three-session plan

Session 2: Toggling Bits · 45 minutes

Focus: toggle6 twice and save results

Checkpoint: 42→44→42.

Session 3: Signed Bits and the Largest Value · 45 minutes

Focus: NOT 255→−256 and choose larger via sign mask

Checkpoint: signed inputs(−5,2) select2 only within the specified safe small comparison range.

Support and differentiation

binary counters/cards and one bit at a time before full masks.

Extend the thinking

explain why NOT twice restores255, and why a sign-mask method is unsafe for arbitrary huge differences.

Assessment evidence

worked binary table, reversible-change explanation, and a tested largest-value program with an explicit range limit.

Print student worksheetView answer key

Curriculum mapping notes

OpenKernel EDU aligns with concepts in the following frameworks. These connections support teacher planning. Check your current local grade or course expectations and assessment requirements when selecting activities.

Ontario

Coding and computational thinking in elementary mathematics; algorithms, programming, data representation and computer systems in secondary computer studies/digital technology contexts.

Units 1–3 address state/data/computers, 4–8 sequence/control/algorithm/debugging/representation, and 9–10 decomposition/systems/projects. Select actual grade/course expectations locally. This model does not establish coverage of all mathematical, digital citizenship, hardware-building or networking outcomes.

British Columbia

Applied Design, Skills and Technologies learning through designing, testing and refining solutions; secondary computer studies/programming concepts involving algorithms, data and computer systems.

Units 4–10 support iterative program design and explanation; units 1–3, 8 and 9 support data/state/system representation. Paper design, trace evidence and reflection make the process visible. Check current grade/course wording; not every ADST competency is covered.

Alberta

Computing science in applicable science/programming contexts; senior-high Career and Technology Studies Computing Science (CSE) concepts in algorithms, structured programs, data and systems.

Units 1–8 develop state, control and abstraction; units 9–10 apply decomposition and testing. Check the current program of studies and course requirements when deciding which activities suit your class.

Selected CSTA 2017 connections

These concept references use the CSTA 2017 framework. Check the current adopted edition and the full standard’s grade-level scope before using an identifier in a formal school mapping.

  • 1B-AP-10 — Sequences, events, loops and conditionals in programs. Aligns with units 1, 4, 5, 9 and 10. Simulated events are distinguished from a physical-device event system.
  • 2-AP-12 — Combinations of control structures in programs. Aligns with units 4–7 and 10 through decisions, loops and calls. Use the complete standard when planning work on compound conditionals or other nested control structures.
  • 2-AP-13 — Decomposing problems and subproblems into manageable parts. Aligns with units 6, 7, 9 and 10 through algorithm roles, reusable services and partitioned work.
  • 2-AP-14 — Reusable procedures and parameters for organizing code. Aligns with units 7 and 10. The VM uses register-passed input/result conventions, rather than high-level parameter declarations.
  • 2-AP-17 — Systematic testing and refining with a range of test cases. Aligns with checked challenges when paired with prediction, debugging explanations and varied cases. A pass alone does not demonstrate the complete standard.

Units 1–3, 8 and 9 also connect to the Computing Systems concept. Algorithm, state, debugging, abstraction and control describe the ideas taught in this resource; consult the local framework for its expectation names and scope.

Official source landing links

Use these official landing pages to check the current adopted edition and local grade or course expectations.