Teaching-mechanic library

current_junction · engineering · balance.ledger

Concept: KCL

Player does: Balance every junction: current in = current out

Breaks: Current gets used up at junctions

Kirchhoff's current law says current in equals current out at every junction; none of it is consumed there.

voltage_loop · engineering · balance.ledger

Concept: KVL

Player does: Make rises and drops around the loop sum to zero

Breaks: Voltage is the same everywhere in series

Kirchhoff's voltage law says the rises and drops around a loop sum to zero, so voltage drops across each series element.

network_compression · engineering · tuner.formula

Concept: Equivalent resistance

Player does: Collapse the resistor network; predict the single equivalent

Breaks: Parallel resistors add up

Parallel resistors combine by reciprocal sum, which always gives a smaller equivalent resistance than any branch, not a sum.

capacitor_reservoir · engineering · tuner.formula

Concept: RC charging

Player does: Choose the wait so the capacitor reaches 63% (one τ)

Breaks: Capacitors charge linearly

A capacitor charges exponentially, approaching its final voltage faster at first and more slowly over time.

logic_factory · engineering · builder.circuit

Concept: Logic gates

Player does: Wire gates so the output matches the target truth table

Breaks: You need AND, OR, and NOT to build any circuit

NAND alone is functionally complete, so every logic circuit can be built from NAND gates without AND, OR, or NOT.

state_explorer · engineering · builder.circuit

Concept: Truth tables

Player does: Test every input combination and fill the table

Breaks: Checking a few inputs proves the circuit

A circuit is verified only by testing every input combination in its truth table, not a sample of them.

grouping_territory · engineering · builder.tiles

Concept: Karnaugh maps

Player does: Cover the 1-cells with the fewest power-of-two rectangles

Breaks: Groups can be any size

Karnaugh map groups must be a power-of-two size (1, 2, 4, 8…) to correctly simplify the expression.

signal_railway · engineering · transformer.trace

Concept: Multiplexers

Player does: Set select lines so the right input track reaches the output

Breaks: Select lines carry the data

Select lines only choose which data input is routed through; they never carry the data themselves.

one_bit_room · engineering · transformer.trace

Concept: Flip-flops

Player does: Predict the stored bit after each clock edge

Breaks: Outputs change whenever inputs change

A flip-flop's stored output changes only at a clock edge, not whenever its inputs change.

safe_sampling_window · engineering · mapper.number_line

Concept: Setup & hold time

Player does: Place the input transition outside the window around the clock edge

Breaks: Any change before the edge is safe

A signal must be stable through both the setup time before and the hold time after the clock edge to be sampled safely.

instruction_factory · engineering · builder.tiles

Concept: Pipelining

Player does: Schedule instructions into stages; count total cycles

Breaks: Pipelining makes each instruction faster

Pipelining raises instruction throughput by overlapping stages; it does not shorten any single instruction's latency.

datapath_relay · engineering · sequencer.linear

Concept: Instruction execution

Player does: Route an instruction through fetch, decode, execute, memory, write-back

Breaks: The PC changes only on jumps and branches

The program counter advances after every instruction, not only on a jump or branch.

memory_distance · engineering · sequencer.rank

Concept: Memory hierarchy

Player does: Rank storage by latency and capacity

Breaks: Bigger memory is faster

Memory hierarchy trades capacity for speed: the fastest tiers, like cache, are the smallest.

path_prediction · engineering · simulator.sample

Concept: Branch prediction

Player does: Guess each branch; watch the pipeline flush on a miss

Breaks: Mispredictions cost nothing

A branch misprediction forces the pipeline to flush and restart, costing real cycles.