Lesson Plan

• Describe the binary floating‑point representation and the purpose of normalisation.
• Apply the step‑by‑step process to normalise a decimal number into IEEE‑754 single‑precision format.
• Analyse how normalisation influences arithmetic operations and recognise special cases (zero, denormalised, infinity, NaN).
• Evaluate a given 32‑bit pattern to determine its decimal value.

• Projector or interactive whiteboard
• Slide deck with diagrams and examples
• Worksheets containing normalisation exercises
• Computers with a simple IDE or online binary converter
• Printed handout of the IEEE‑754 single‑precision format table
• Calculator (optional)

Start with a quick poll: “Who has seen unexpected results because of rounding errors in code?” Connect this to prior knowledge of binary numbers and ask students to predict why such errors occur. Explain that today they will learn how normalising floating‑point numbers creates a unique, precise representation, and they will be able to demonstrate the process by the end of the lesson.

1. Do‑Now (5') – Students convert 13.625 and –0.15625 to binary on mini‑whiteboards.
2. Mini‑lecture (10') – Review the IEEE‑754 format, the need for normalisation, and the bias concept using a slide diagram.
3. Guided practice (15') – Walk through Example 1 (positive number) together, filling a table of sign, exponent, and fraction fields.
4. Independent practice (15') – Students normalise a set of numbers (including a small fraction) on worksheets while the teacher circulates.
5. Check for understanding (5') – Quick Kahoot quiz / exit ticket: identify the sign bit and stored exponent for a given 32‑bit pattern.
6. Extension (optional 5') – Discuss special cases (zero, denormals, infinity, NaN) and their relevance to debugging.

Recap the normalisation steps and emphasise how the bias and hidden 1 ensure a unique representation. Students complete an exit ticket summarising one key point they will apply when debugging floating‑point errors. For homework, assign a set of decimal numbers to normalise and ask learners to convert the resulting 32‑bit patterns back to decimal.