Big Idea 2 · Topic 2.1 · Exercise 1
The Wraparound Bug
25 minutes
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Q1 · 3 points on the handout
Incident 5: order LOW (110), MED (1001), and HIGH (1100) from least to greatest WITHOUT fully converting - name the shortcut used for each comparison. Then write the new SEVERE level (decimal 22) in binary and state where it lands in the order.
Q2 · 3 points on the handout
The tracker's optical sensor watches your pulse - a signal that rises and falls smoothly, with infinitely many in-between values - yet the device stores only a list of binary numbers. Name what kind of data the pulse is, name the technique that turns it into bits, and state what the tracker gains by measuring MORE often.
Q3 · 2 points on the handout
ENRICHMENT: The firmware team proposes fixing Incident 1 by widening the step field from 8 bits to 16 bits (maximum 65,535). State the general ceiling for an n-bit field, show what the display would read after an ultramarathoner logs 70,000 steps on the NEW firmware, and explain why 'just add more bits' raises the ceiling but never abolishes overflow as a category.
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