From Light Bulbs to CPUs: Building Logic Gates, Adders, and an ALU from Scratch

1. Encoding and Circuits – Signal Conversion

The story begins with two teenagers who, unable to use their phones at night, devise a secret communication method by representing Chinese characters as sequences of light‑bulb on/off states, reading the bulb status once per second. This illustrates the concept of encoding physical signals into binary information.

2. Logic Gates – Signal Relations

By adding a second switch that must be closed together with the first for the bulb to light, they create a logical relationship between inputs and output, introducing the notion of a logic gate. The two switches act as inputs (0 = open, 1 = closed) and the bulb as the output.

Truth table for an AND gate:

Input A  Input B  Output
0        0        0
0        1        0
1        0        0
1        1        1

They label the circuit as a AND gate and adopt binary notation (1 = connected, 0 = disconnected) for further abstraction.

3. Adders – Signal Computation

To perform arithmetic they explore binary addition. A single‑bit addition table (0+0=0, 0+1=1, 1+0=1, 1+1=10) leads to the design of a half‑adder using an XOR gate for the sum and an AND gate for the carry.

By cascading another half‑adder and an OR gate they obtain a full‑adder , capable of handling the carry from a previous bit.

4. Clock – Oscillating Signal

Adding a feedback loop where closing switch A pulls switch B down, which then opens the circuit and releases B to spring back, creates a self‑oscillating circuit. The alternating on/off pattern is called a clock , and the generated periodic signal is the clock signal .

5. RAM – Storing Signals

To retain data they design a 1‑bit latch: when the data input is 1 and a control pulse transitions from 0 to 1, the output becomes 1 and holds that value until the next control pulse. The same principle with 0 stores a 0. By chaining multiple latches with decoders and selectors they build an 8‑bit random‑access memory (RAM) capable of reading and writing arbitrary addresses.

6. Program – Automation

Introducing a 10‑bit counter (clock‑driven, with a clear input) provides sequential addresses (0‑5) that feed the RAM. Connecting the counter, the ALU, and the RAM enables an automatic accumulation of the stored numbers 1 through 7. The process is described step‑by‑step, showing how each counter value selects a datum, adds it to the running total via the ALU, and stores the intermediate result in the latch.

7. Instruction Set and Control Unit

To make the system programmable they add a second RAM that holds instruction codes. Three instructions are defined:

add – accumulate the value at the current data address.

nop – no operation (disable latch write).

halt – stop the counter (disable count enable).

By mapping instruction RAM addresses to data RAM addresses, the control unit can enable or disable the latch and counter based on the fetched opcode, allowing selective summation and early termination.

With this instruction set, any sequence of add , nop , and halt commands can be programmed to perform arbitrary arithmetic tasks, illustrating the fundamental principles of digital computation, from low‑level hardware to simple software.