How Two Kids Built a 32‑Bit Binary Adder from Scratch

In a second‑grade math class, Xiao Ming struggles with the problem 6324 + 244675 and recalls a finger‑counting method that can represent numbers from 0 to 31 using a single hand.

His classmate Xiao Hong explains that each finger position corresponds to a binary digit, allowing the hand to encode any integer between 0 and 31. Together they sketch a truth table linking finger patterns to binary values.

They imagine a machine with three inputs (A, B, and carry‑in) and two outputs (sum and carry‑out) that could perform binary addition. Xiao Hong introduces the concepts of AND, OR, and NOT gates, describing their behavior with simple switch‑lamp diagrams.

Using a teaching kit containing AND, OR, and NOT gate components, the students build a one‑bit full adder circuit. They connect the gates so that the sum output is 1 when an odd number of inputs are high, and the carry‑out is 1 when at least two inputs are high.

Encouraged by the success of the one‑bit adder, they replicate the circuit 32 times and link the carry‑out of each stage to the carry‑in of the next, forming a 32‑bit binary adder capable of adding large numbers such as 6324 and 244675.

The story concludes with the students marveling at how binary representation, logic gates, and modular circuit design transform a simple finger‑counting trick into a powerful computational device.