How to get an answer out of sand

Sand and metal

We start with quartz, the main ingredient in sand. Quartz is silicon dioxide: one silicon atom for every two oxygen atoms, arranged in a repeating crystal structure. Our first task is to separate the silicon from the oxygen.

We heat the quartz with carbon to extract silicon, then purify it. We melt the purified silicon and grow it into one large crystal, called an ingot.

We then slice the ingot into thin wafers: the blank canvases for our chips.

We can change how silicon conducts electricity by adding small amounts of other elements. This is called doping. Here is a cross-section of our wafer, lightly doped with boron which was mixed into the liquid silicon before crystal growth.

We can also implant dopants into selected parts of the wafer by firing electrically charged atoms into the silicon. Here we create two pockets of phosphorus-doped silicon within the boron-doped silicon. Phosphorus and boron respectively donate and accept electrons. By carefully arranging distinct regions of silicon doped with these two elements, we can shape how current flows.

We can now build our first transistor. We add a wire to each of the two pockets and place a third wire, called the gate, above the silicon between them. The gate is slightly separated from the silicon, allowing it to control the flow of current between the other wires without making direct contact.

A voltage difference can drive electrons through a circuit. Let us hold the left wire at 0 volts and the right wire at 1 volt. For electrons, higher voltage means lower energy, so picture the 0-volt side as higher ground and the 1-volt side as lower ground. Electrons would flow downhill from left to right, but a hill between the two pockets blocks their path. The gate lets us lower this barrier and allow them through.

With the central gate also at 0 volts, this barrier is high and electrons struggle to flow between the two pockets.

Raising the gate to 1 volt lowers this barrier, opening a conducting path between the pockets. Electrons can now flow through the transistor and around a connected circuit, lighting a bulb. This is the basic picture of an n-type MOSFET, an electrically controlled switch with no moving parts. With no mechanism to move, the switch can be built as a microscopic pattern of materials and repeated billions of times across a chip.

We now have a switch that we can control with a voltage input. To make larger circuits easier to draw, we will represent each transistor with a simple symbol, shown on the left. On the right, we show what this switch does. With its gate at 1 volt, it connects the two ends like an unbroken wire. With its gate at 0 volts, the connection is broken. The gate controls this connection without joining it.

Wires connected through an on switch share the same voltage. Connecting a wire to a supply held at 1 volt brings it to 1 volt, and connecting it to a supply held at 0 volts brings it to 0 volts. An off switch keeps the two sides separate.

We can also make a p-type MOSFET by swapping the two types of doped silicon. In the circuits we are about to build, the n-type switch turns on for an input of 1 volt and off for 0 volts, while the p-type does the reverse. The small circle on its gate distinguishes the p-type symbol. We now have two switches that respond in opposite ways to the same input.

The next step is to combine these switches into larger and larger structures so that, together, they can calculate, remember and think. We will build towards these abilities one layer at a time, showing how each new structure makes more complex tasks possible.

Logic

To calculate with electrical signals, we first need a way to represent information. We use a low voltage to represent 0 and a high voltage to represent 1. Each of these binary digits is called a bit.

By connecting transistors, we can build circuits called logic gates that turn input bits into output bits according to a simple rule. The simplest example is the NOT gate, which flips its input. A 0 becomes a 1, and a 1 becomes a 0.

Let’s zoom out one step and connect two transistors to make our first logic gate. The top bar is held at 1 volt and the bottom bar at 0 volts. Our input A controls both gates, and the output Ā is the wire joining the two transistors.

When A is 0, the p-type switch is on and the n-type is off. The output is connected to the top bar, so it settles to 1. When A is 1, their roles reverse and the output connects to the bottom bar, settling to 0. The output is always the opposite of the input. We have made a NOT gate.

Add two more transistors and we can give our circuit two inputs, A and B. Each input controls one p-type switch and one n-type switch. The two p-type switches at the top are connected one after another, so both must be on to connect the output to 1. The two n-type switches at the bottom are side by side, giving two separate routes to 0. Either one can make that connection.

When both inputs are 0, both p-type switches are on and both n-type switches are off. The output connects to the top bar and becomes 1. If either input is 1, its p-type switch breaks the upper path while its n-type switch connects the output to the bottom bar, making it 0. This is a NOR gate. Its output is 1 when neither A nor B is 1.

Now rearrange the same four transistors. Put the two n-type switches one after another and the two p-type switches side by side. The output can reach the bottom bar only when both n-type switches are on, which requires both inputs to be 1. It then becomes 0.

If either input is 0, its n-type switch breaks that lower path and its p-type switch provides a connection to the top bar. The output becomes 1. This is a NAND gate. Its output is 1 when A and B are not both 1 simultaneously.

A truth table lists the output for every possible combination of inputs. These tables collect the rules we have just built from switches.

NOT

NOR and NAND

Let’s zoom out again and give this four-transistor NAND circuit a symbol. The two inputs enter on the flat side, and the output exits after the small circle.

It can be shown that NAND gates alone can be combined to implement any function that maps a finite set of input bits to output bits. In other words, we can specify a truth table and build a circuit that follows it using only NAND gates. One NAND with its two inputs tied together makes NOT. Two make AND by using the second to invert the first’s output. Three make OR by inverting each input before feeding them into the third. A fourth inverts that result to make NOR. NOT, AND and OR are enough to build any truth table, so NAND alone is enough too.

This makes NAND gates universal building blocks. From this one simple circuit, we can build the logic for everything from a calculator to a computer running an AI model.

Arithmetic

Let’s zoom out further and combine NAND gates into a circuit that adds. In binary, we have only two digits, 0 and 1, so adding 1 and 1 gives 10. We write down 0 and carry 1 into the next column, just as we carry digits in ordinary addition.

Our circuit handles one column at a time. It adds two input bits, aᵢ and bᵢ, along with any carry from the previous column, cᵢ. It produces the answer bit sᵢ and a carry for the next column, cᵢ₊₁. This three-input, two-output circuit is called a full adder.

Connect several full adders in a row, passing each carry cᵢ₊₁ into the next column, and we can add entire binary numbers. Here, four adders calculate 0011 + 0110 = 1001, or 3 + 6 = 9. More columns let us work with larger numbers. With addition as a building block, it is a short step to circuits that subtract and multiply, and our toolset has grown.

We have combined small groups of transistors into a circuit that adds numbers, but each calculation has a physical cost. Every calculation involves voltage flips as some of the transistors switch. These flips charge or discharge the tiny capacitances of the transistors and wires, expending energy that is dissipated as heat.

The faster we switch, the more heat we produce each second. This switching power scales with CV²f, where C is the capacitance being switched, V is the voltage swing, and f is the clock speed, which sets the pace of computation. Smaller capacitances and lower voltages reduce the energy needed, while switching less often reduces the rate at which we generate heat. Heat is a budget we will keep encountering as the transistor populations climb.

Memory

We can now calculate an answer, but how do we remember it? Let’s zoom back in and connect a few NAND gates so that their outputs feed back into their inputs. This circuit is called a latch. It has a data input D, a write-enable input WE, and an output Q. While WE is 1, Q becomes D. When WE becomes 0, Q holds its last value, even if D changes.

How does a loop create memory? The two gates on the right feed their outputs into each other, each reinforcing the other’s state. With writing disabled (WE = 0), this feedback holds Q at its last value for as long as power is supplied. We have added memory to our toolset.

Let’s zoom out again and place four latches side by side, each holding one bit. Together, they form a four-bit register that can remember a four-bit binary number. By sharing a write-enable signal, all four latches can copy their inputs at D simultaneously, then hold the number while those inputs change.

We can now connect our register to the four-bit adder. With write-enable at 1, the register copies the answer, 1001. Set write-enable to 0 and that answer is held. The adder can calculate something new while the register remembers the previous result. We can now both calculate and keep the answer.

As circuits become larger and more complex, timing challenges appear to show. Changing an input does not change every part of a circuit at once. The change takes time to spread, and different values settle at different moments. These delays can result in incorrect information processing as old data gets used for computation, or glitches.

We now have circuits that calculate and circuits that remember. Our next step is to combine them into a machine that follows instructions, choosing which values to use, what to calculate, and where to store each result.