Physical MUX Tiles: A Hands-On Logic Alphabet For EE Education

Physical prototype first published January 31, 2026

STEM electrical engineering · tangible logic · PCB prototype

Boolean circuit structure becomes a model a learner can hold, read, rotate, assemble, and change.

The physical MUX tiles turn selectors, inputs, constants, routes, and intersections into a connectorized PCB alphabet. Circuit role, orientation, topology, and assembly geometry are visible in the same piece.

This is a standalone teaching prototype and physical-computing project. It is related to the MUX-first path into FPGA LUTs and Cartilage, but it is not evidence of the complete Cartilage architecture.

A hand holds a two-level assembly of purple three-lobed circuit boards with soldered contacts and black connectors
The larger hand-built assembly: repeated PCB outlines, visible signal roles, soldered contacts, and connector-spaced layers at palm scale.

The Achievement Is A Physical Language

For roughly twenty-five years, the idea moved through mental models, paper, and CAD before the first connectorized batch could be snapped into a patch and picked up as one object.

The important crossing was not merely from an unmade board to a made board. It was from symbols that only existed in a drawing to a set of parts whose roles, sides, rotations, and neighbor relationships remain legible after assembly.

The circuit diagram and the manipulable physical representation become the same thing.

The Alphabet

Loose purple three-lobed PCB variants with plated contacts and labels including INPUT, CONST_0, CONST_1, I0, I1, and S
Several signal-role variants share one three-lobed mechanical outline while their traces and labels make the logical role visible.

Connector Geometry Makes Orientation Real

A schematic symbol can be rotated without consequence unless the reader keeps track. Here the connector side, contact groups, physical rotation, and neighboring pieces are all part of the object. The assembled structure can be inspected from several angles while its topology remains visible.

Purple circuit boards arranged at two heights and joined by black socket connectors
An early connector-stacked assembly showing the actual socket geometry and static vertical separation.
A hand holds the purple PCB assembly edge-on, showing two board levels separated by black sockets
Side profile of the assembled prototype, with its thickness, board spacing, and connector height visible.

A Proposed Hands-On EE Learning Path

The project is designed to let a learner move from one physical decision to a circuit they can later express in Logisim, a truth table, or FPGA RTL. This teaching sequence is proposed; classroom outcomes have not yet been measured.

  1. Name The Ports

    Find I0, I1, S, input, constant, and route roles directly on the boards.

  2. Predict One Selection

    Choose values for the two MUX inputs and selector, then state which physical route should reach the output.

  3. Rotate And Compose

    Change the orientation of a piece, identify its new neighbors, and explain what topology changed.

  4. Trace A Value

    Follow a constant or input through route and intersection pieces without collapsing the patch back into an invisible netlist.

  5. Build A Combinational Patch

    Use several pieces to represent a small Boolean function, write its truth table, and reproduce it in Logisim.

  6. Move From MUX To LUT

    See how one selector becomes LUT1, how more address bits grow the stored truth table, and how the idea reaches real FPGA LUT4, LUT5, and LUT6 structures.

The Bridge To FPGA Logic And Cartilage

From Logisim And Multiplexers To LUT1–LUT6 is the direct conceptual continuation. It begins with a visible 2:1 MUX, grows the selector into a stored truth table, and connects LUT4 to Lattice iCE40 and LUT5/LUT6 to AMD/Xilinx configurable logic.

The complete Cartilage learning path continues into CMOS gain, output drive, clock and event distribution, statecharts, one-hot machines, timing closure, metal routing, nested components, and runtime instantiation in adjacent space. Those are logical and architectural layers beyond what these photographs establish.

What The Physical Evidence Establishes

EstablishedFabricated role variants share a repeated outline; plated contacts and socket/header parts are exposed; multiple pieces compose into palm-scale assemblies; static connector spacing permits more than one elevation.

Still to establish: powered electrical operation, full connection correctness, timing, signal integrity, insertion-cycle reliability, a powered sequential patch, classroom outcomes, safety certification, manufacturing scale, and production readiness.

The next decisive electrical result is deliberately small: power a patch and demonstrate a sequential circuit, with the D-flip-flop as the existing target. The current photographs are valuable because they prove the alphabet crossed into physical composition; they do not need to pretend that the next milestone already happened.

Source And Provenance

The physical alphabet was first published in the dated note The Physical MUX Tile Alphabet. The article here restores the original project arc, adds the fabricated-part photography, and gives the teaching project its own stable front door.

The photographs are published from the supplied project archive as cropped, metadata-free WebP derivatives. The original source files remain unchanged in the project package.