Build a Physical Binary Counter
How computers count everything using nothing but on and off — made physical with 4 cups.
Related field: Computer Engineering
Mission Briefing
Objective
Build a physical 4-bit binary counter and manually count from 0 to 15 in binary, in the correct order, without an error.
Constraints
- Must use exactly 4 physical objects, each able to show only two states (like a cup right-side-up vs. upside-down, or a card face-up vs. face-down)
- Must count in the correct binary order without skipping a combination
- No calculator or written conversion chart allowed while counting — figure out each step by the counting rule itself
Concept You're Testing
Binary representation — computers store and process every number, letter, and instruction using only two states (0 and 1). Four bits can represent exactly 16 different values (2 to the power of 4), which is why more bits means a computer can represent bigger numbers or more possibilities.
What You'll Need
- 4 cups, cards, or coins, each flippable between two distinct states
- A flat surface to line them up
Instructions
- 1Line up your 4 objects in a row. Decide which state means "1" (like right-side-up) and which means "0" (like upside-down).
- 2Start with all 4 showing "0" — this represents zero.
- 3To count up by one: flip the rightmost object. If it was already "1," flip it back to "0" and carry the flip to the next object to its left, repeating that rule as needed.
- 4Continue counting up one at a time, writing down each combination as a sequence of 1s and 0s.
- 5Keep going until you reach 1111 (all four showing "1") — this should be your 16th combination, representing 15.
- 6Check your sequence: every combination from 0000 to 1111 should appear exactly once, in order.
How to Measure Results
Successfully produce all 16 unique combinations (0000 through 1111) in the correct counting order, with no repeats and no skipped combinations.
Skills You'll Practice
- What binary numbers actually are, physically, not just as abstract 1s and 0s
- Why 4 bits means exactly 16 possible values, and how that scales as you add more bits
- The "carry" rule that makes counting in binary work, which is the same logic a computer's hardware uses
- Careful, systematic tracking of a repeating rule without making an error
If It Doesn't Work the First Time
That's normal — this challenge follows the same design process real engineers use. A failed test just tells you where to go back and improve.
Figure out what problem you're actually solving, and what would even count as success. Skip this step and jump straight to building, and a lot of bad designs happen right here.