One plus one becomes ten.: sources & model

Flip real input bits on a little calculator. Build a result from simple rules, and follow a carry as it crosses four columns.

What supports the explanation?

What this model assumes

1. Exact Boolean arithmetic with two unsigned 4-bit operands and one carry-in. No signed numbers, clocks, memory, transistor voltages or propagation-delay simulation.
2. The calculator is an illustrative application. Its visible adder is not a teardown of a particular product.
3. Changing an input restarts the dependency sequence. The settled result remains labeled separately from the revealed columns.
4. The equations: For inputs A, B and Cᵢₙ: S=A XOR B XOR Cᵢₙ. Cₒᵤₜ=(A AND B) OR (Cᵢₙ AND (A XOR B)). Every one of the eight input combinations is defined.
5. Keep the width visible: Two unsigned four-bit numbers and one carry-in can sum to 31. That needs five bits: 11111. Silently discarding the fifth bit would wrap the result modulo 16. This lesson keeps it.
6. A bit is a represented state: A logic 1 is not universally 1 volt. Real devices specify valid voltage ranges, loading and delays. The highlights here show evaluation order, not electrons, wire speed or measured nanoseconds.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

The topic card uses an AI-generated editorial illustration. It introduces the subject; it is not a validated anatomical reference or a measured landscape. The experiment’s diagrams, readouts and assumptions explain the model separately.