The p-n junction — a diode
- Current
- —
- Depletion layer
- —
- State
- —
Model of an ideal silicon diode (Shockley equation, Is = 10⁻¹⁴ A, room temperature). A real diode also has resistance and a small leakage current in reverse bias.
The MOSFET as a switch
- Threshold UP
- 0.70 V
- Drain current
- 0.0 mA
- Channel
- none
- Switch
- open
Simplified model: below the threshold the current is ≈ 0, above it I ≈ ½·k·(UG − UP)², limited by a resistor to 20 mA. In a processor the transistor works as a switch: either “open” or “closed”.
Moore’s law
tap a point · ←/→From vacuum tubes to billions of transistors
- The vacuum tube (Fleming’s vacuum diode), and in 1906 the triode — the first electronic “switches.” Hot, big, and unreliable.
- ENIAC: about 18,000 tubes, about 27 tons. Some tube was always burning out.
- John Bardeen and Walter Brattain at Bell Labs build the point-contact transistor; William Shockley soon develops the junction transistor. All three share the Nobel Prize in Physics in 1956.
- Jack Kilby (Texas Instruments) — the first integrated circuit (made of germanium); in 1959 Robert Noyce (Fairchild) — the planar silicon chip, ancestor of today’s chips.
- Intel 4004 — the first single-chip microprocessor: about 2,300 transistors.
- The largest processors and graphics cards have tens or even hundreds of billions of transistors.
A Polish connection: Jan Czochralski. In 1916 he discovered a method of pulling a crystal out of molten metal. Today almost all single-crystal silicon for electronics is grown this way — cylinders up to 30 cm across, sliced into the wafers that become processors.
A gate made of transistors
flip the inputs and watch which transistors conduct
CMOS circuit
The same as switches
transistors: 2
The upper network (pMOS) connects the output to the positive supply, the lower one (nMOS) to ground. Exactly one of them conducts at any time, so the output is a clean 0 or 1, and at rest almost no current flows. That is the idea of CMOS — nearly every processor today is built this way.
Gate sandbox
Circuit truth table
Everything from NAND
The NAND gate is universal: you can build any other gate out of NANDs alone. Use only NANDs (plus switches and LEDs) and tick off the goals:
NOTANDORXOR
Hint for XOR: 4 NAND gates are enough. The first one gets A and B, and its output goes to the next two…
Counting in binary
keys 1…8 flip the bits (1 = 128)
8 bits make a byte: 2⁸ = 256 different values (0–255). Each bit is worth twice as much as the bit to its right — just like in decimal, only with base 2 instead of 10.
An adder made of gates
8-bit adder
A
B
Subtraction without a separate circuit: A − B = A + B + 1 (two’s complement). XOR gates invert the bits of B, and the carry-in adds the one.
SR flip-flop from two NORs
Feedback: output Q goes back to the input of the other gate and keeps itself going. That is how 1 bit of memory is born — the circuit “remembers” what it was last told, even after you let go of the button.
The clock
D flip-flop
Q =
Counter
0 = 0000
4-bit register
Q:
Everything changes exactly at the moment the clock goes from 0 to 1 (the rising edge). That is how billions of flip-flops in a processor stay in step, like an orchestra following the conductor’s baton.
Gigahertz up close
- One tick lasts
- —
- Light in one tick
- —
- Ticks per second
- —
RAM
16 cells of 8 bits each. The address decoder selects one row, and the whole byte is written or read at once.
Address
Data
8-bit processor
Display (OUT)
Program
label: instruction argument ; comment
Instruction set
Each instruction is one byte: the upper 4 bits are the opcode, the lower 4 are a cell address (0–15) or a small number. In parentheses: other names that also work, including the original Polish ones.
How does this scale up to a real processor?
Wider words64 bits instead of 8, and billions of memory cells instead of 16.
PipelineWhile one instruction is executing, the next is already being decoded and the one after that fetched — like an assembly line in a factory.
CacheRAM is slow for a processor, so the most frequently used data are kept in fast cache memory right next to the core.
Many coresSeveral, a dozen or even more processors on one chip — and in graphics cards, thousands of simpler units working at once.
The principle stays the same: fetch an instruction, decode it, execute it — billions of times per second. You can explore the sequence from the Fibonacci example in the Fibonacci experiment.
Text → bits
Every letter is a number, and a number is bits. Letters beyond plain ASCII — such as the Polish ą or ł — take 2 bytes each in UTF-8.
Pixels and colors
A screen is a grid of pixels. Each pixel is three bytes: how much red, green, and blue (RGB).
Compression in one sentence
Instead of repeating the same thing, write down “how many times”: that is how the simplest compression, RLE, works.
JPG, MP3, or ZIP are much cleverer, but the idea is the same: don’t store what can be predicted.
The speed of light is a limit too
In optical fiber a signal travels at about 200,000 km/s — roughly ⅔ of the speed of light in a vacuum.
Enigma and the Polish mathematicians
At the end of 1932 Marian Rejewski of Poland’s Cipher Bureau, using permutation theory (and documents obtained by French intelligence), reconstructed the rotor wiring of the German Enigma. Together with Jerzy Różycki and Henryk Zygalski he developed methods for breaking the keys: the cyclometer, Zygalski sheets, and the “cryptologic bomb” (1938). In July 1939 the Poles handed their knowledge over to the French and the British; at Bletchley Park, Alan Turing and his colleagues built on these ideas.
Cipher
A toy model: rotors I-II-III, reflector B, setting AAA, no plugboard. Notice: the same letter encrypts differently every time, but never to itself — that was Enigma’s weakness.
Turing and computability
In 1936 Alan Turing described an imaginary machine with a tape and a head that can compute anything that can be computed at all — and proved that there are questions no program can answer (for example, whether an arbitrary program will ever stop).
Your mini processor from mode 5 — given unlimited memory — could do everything any supercomputer can, just more slowly.
Timeline: from ENIAC to the smartphone
- Turing machine — a mathematical model of a computer.
- ENIAC (USA) — an electronic computer with about 18,000 tubes; unveiled to the public in 1946.
- The transistor at Bell Labs.
- UNIVAC I — one of the first computers sold to businesses and government offices.
- XYZ — regarded as the first working Polish digital computer; built by Leon Łukaszewicz’s team in Warsaw (the Mathematical Apparatus Group of the Polish Academy of Sciences). Vacuum-tube based.
- The integrated circuit (Kilby); a year later, in silicon (Noyce).
- Odra — starting with the Odra 1001 prototype, the Elwro works in Wrocław built a series of computers for years; later models of the 1300 series were compatible with British ICL machines.
- ARPANET — the first message between two computers of the network that grew into the Internet.
- Intel 4004 — a processor on a single integrated circuit.
- IBM PC — the personal computer that became the standard.
- WWW — Tim Berners-Lee at CERN puts the first web pages online.
- The iPhone and the smartphone era: more power in your pocket than in the supercomputers of old.