How It Works: The Full Stack

The project is organized into a vertical flow, making it easy to trace the signal from input to result:

  • Invoeren (Input): Two keyboards allow you to select two numbers between 0 and 7.
  • Decimaal (Decimal Indicator): Yellow LEDs provide immediate feedback on which decimal numbers were selected.
  • Coderen (Binary Encoding): A diode matrix converts the decimal input into 3-bit binary signals.
  • Binair (Binary State): Red LEDs display the "raw" binary bits before they enter the arithmetic unit.
  • Versterken (Amplification): To ensure the logic signals have enough "oomph" to drive the subsequent stages, a ULQ2003 amplifier works alongside power relays to boost the signal.
  • Optellen (The Adder): This is the heart of the machine. It uses one half-adder (for bit 0) and two full-adders (for bits 1 and 2) constructed from Omron G5V-2 relays. This stage calculates the sum and manages the carry-out bits.
  • Decoderen (Binary-to-Decimal): A relay-based demultiplexer takes the binary sum (which can now be as high as 14) and converts it back into a decimal signal.
  • 7-Segment Encoding: A final diode matrix maps the decimal result to the specific segments (a-g) of the output display.
  • Tonen (The Result): A large 7-segment display reveals the final sum.

How the binary adder works

The diagram shows a 1‑bit full binary adder, which adds two binary inputs (a and b) together with an incoming carry (Cin). The circuit produces two outputs: the sum bit (C) and the carry‑out (Cout).

First, the inputs a and b are combined using both an XOR and an AND operation. The XOR gate generates the preliminary sum (a ⊕ b), while the AND gate generates a carry if both inputs are high (a ∧ b).

Next, the incoming carry (Cin) is added to this preliminary sum. Again, an XOR operation produces the final sum bit (C), and an AND operation detects whether this second addition generates a carry.

Finally, the two possible carry signals are combined to form the output carry (Cout). This means Cout goes high if either:

  • a and b are both high, or
  • Cin is high while a ⊕ b is high

In logical terms:

  • C = a ⊕ b ⊕ Cin
  • Cout = (a ∧ b) ∨ (Cin ∧ (a ⊕ b))

By cascading multiple identical stages, this 1‑bit adder can be extended to form a multi‑bit binary adder.

Technical Highlights

  • Relay Logic: The arithmetic is performed using classic relay logic, where two half-adders are combined to create a full-adder.
  • Diode Matrices: Rather than using integrated circuits, the "programming" for the 7-segment display and the decimal-to-binary conversion is handled by large, visible diode grids.
  • The "Clack" Factor: Every calculation is accompanied by the rhythmic sound of mechanical switching, turning math into a tactile experience.

Why Build This?

It’s designed to pull back the curtain on digital computation. By separating the encoding, arithmetic, and decoding into distinct, LED-monitored layers, it becomes a powerful educational tool for anyone wanting to understand how computers actually compute at the most basic level.

This project is part of my four‑project series “My Relay ADDiction” (pun intended): a hands‑on exploration of logic and arithmetic built with relays, diodes, LEDs, and a healthy amount of curiosity.

Each project stands on its own, but together they form a learning path—from basic binary gate behavior (It’s logic!), through number representation (TritBits), to full adders in both binary and balanced ternary.

Related projects in the series: 

 • It’s logic! – https://hackaday.io/project/184752 

 • Visual Binary Adder – https://hackaday.io/project/205210 

 • TritBits – https://hackaday.io/project/205130 

 • Balanced Ternary Relay Adder – https://hackaday.io/project/205212