Light the Lamp is a free puzzle game about logic gates, the tiny switching circuits that every computer is built from. Flick the switches to make each lamp match its goal. The game starts with a single wire and adds one new part at a time: NOT, AND, OR, NAND, NOR, XOR and XNOR gates, then circuits that add numbers, choose between signals and remember. There are 37 levels in 11 chapters, and every gate shows its truth table when you tap it.

How to play

• Press a switch to turn it on (1) or off (0). Wires that are on glow orange.
• Each lamp has a tag that shows its goal, ON or OFF. The tag turns green with a tick when the lamp matches it. Make every lamp match its tag to solve the level.
• A switch with a padlock can’t be changed.
• Try to solve each level in the fewest presses. The fewest possible is shown under the board, and matching it earns a gold star.
• Tap any gate to see its truth table, with the row it is using right now highlighted.
• In the “Choose the gate” chapter, a dashed box is an empty socket. Press it to put a gate in, and keep pressing to try others. The table under the board must show a tick on every row.
• Tick “Show 1s and 0s” to see the value on every wire.

The game works with a mouse, a touchscreen or a keyboard (press Tab to move to a switch, then Space or Enter). On a phone the circuits run from top to bottom. Your progress is saved in your browser, so you can come back to it later. The Levels button lists every level, and the first level of each chapter is always open if you want to skip ahead.

What is a logic gate?

A logic gate is a small circuit with one or more inputs and one output. Each input and output is either 1 (on, a high voltage) or 0 (off, a low voltage), and the gate works out its output by a fixed rule. Inside a chip, each gate is a handful of transistors used as switches. Join enough gates together and you get circuits that add, compare, choose and remember, which is everything a processor does.

A truth table lists a gate’s output for every combination of its inputs. A gate with two inputs has four combinations (00, 01, 10 and 11), so its truth table has four rows.

The seven logic gates

These are the gates in the game, with their outputs for each pair of inputs and a real chip that contains them. The chips are from the 74HC family, which runs on 2 to 6 volts.

On a circuit diagram, a small circle on a gate’s output means NOT, which is how NAND, NOR and XNOR are drawn. In Boolean algebra, AND is often written A·B, OR is written A + B, XOR is written A ⊕ B, and a bar over a letter means NOT.

XOR (exclusive OR) is the one that catches people out. An ordinary OR gives 1 when one input or both inputs are 1; XOR gives 1 only when exactly one of its two inputs is 1. With three or more inputs, XOR gives 1 when an odd number of them are 1, which is why it is used for parity checks that spot a flipped bit in stored or sent data.

Why NAND and NOR are called universal gates

You can build any digital circuit from NAND gates alone, or from NOR gates alone. The game shows how in chapter 6:

• A NAND gate with its two inputs joined together is a NOT gate (“NAND as NOT”).
• A NAND gate followed by that NOT is an AND gate (“AND from NANDs”).
• NOT gates in front of a NAND gate’s inputs make an OR gate (“OR from NANDs”).

The last one works because of De Morgan’s laws. NOT (A AND B) is the same as (NOT A) OR (NOT B), and NOT (A OR B) is the same as (NOT A) AND (NOT B). The “Neither” level shows the second law: its two lamps always match, one driven by a NOR gate and one by two NOT gates and an AND gate.

The idea is not just a classroom trick. The Apollo Guidance Computer, which helped to fly astronauts to the Moon, had a processor built entirely from NOR gates, with two 3-input NOR gates on each chip.

How gates add numbers

Binary numbers use only the digits 0 and 1, and each column is worth twice the column to its right. Adding two single bits gives these answers:

The sum column is exactly XOR, and the carry column is exactly AND, so one XOR gate and one AND gate add two bits. That circuit is called a half adder. A full adder also adds a carry from the column before, using two XOR gates, two AND gates and an OR gate (the “Full adder” level). Line up one full adder per column, with each carry out feeding the next carry in, and you can add numbers of any size. A 74HC283 chip adds two 4-bit numbers like this, with extra gates that work out the carries faster.

How a latch remembers

Every circuit in the first ten chapters forgets: change a switch and the lamps change straight away. The memory chapter uses feedback instead. In an SR latch, two NOR gates each feed their output into one of the other’s inputs:

• Turn S (set) on and the lower gate’s output drops to 0, so the upper gate’s output, Q, rises to 1. Q then holds the lower gate at 0 by itself, so Q stays on after S goes off again.
• R (reset) does the opposite and turns Q off.
• With both off, the latch keeps whatever it was last set to. Turning S and R on together is not allowed in a real latch: both outputs go to 0, and the result when you let go depends on which switch goes off first.

A D latch adds two AND gates and a NOT gate in front, so there is one data input, D, and an enable input, E. While E is on, Q copies D; when E goes off, Q keeps the last value of D. Eight D latches side by side store one byte, and the 74HC373 chip has exactly that: eight D latches in one package. Registers in a processor are built from circuits that work in a similar way.

Build a level with real chips

Any level in the game can be built on a breadboard. Here is the “Both at once” level (one AND gate, two switches and a lamp) with real parts:

• a 74HC08 chip (four AND gates)
• a 5 V supply, such as a USB breadboard power module
• two switches or push buttons
• two 10 kΩ resistors
• an LED and a 1 kΩ resistor

1. Fit the chip across the gap in the middle of the breadboard. Connect pin 14 to +5 V and pin 7 to 0 V.
2. Pins 1 and 2 are the inputs of the first gate. Wire each one to +5 V through a switch, and also to 0 V through a 10 kΩ resistor. The resistor holds the input at 0 when the switch is open. CMOS chips like this must never have an input left unconnected, because a floating input can make the chip misbehave and draw extra current, so connect the inputs of the three unused gates (pins 4, 5, 9, 10, 12 and 13) to 0 V as well.
3. Pin 3 is the output. Connect it to the LED’s longer leg, and the LED’s shorter leg to 0 V through the 1 kΩ resistor. With a red LED that keeps the current to about 3 mA, which is plenty for a modern LED and well inside what the chip can supply. Our LED resistor calculator works out the resistor for other LEDs and supplies.
4. Close both switches and the LED lights. Open either one and it goes out.

Swap the 74HC08 for a 74HC32 and the same circuit becomes OR; a 74HC86 makes it XOR, and a 74HC00 makes it NAND. Those chips use the same pins as the 74HC08, but the 74HC02 (NOR) does not: its first output is pin 1 and its inputs are pins 2 and 3. Always check the pin diagram in the datasheet before you wire a chip. If you are new to breadboards, start with our guide to making a simple LED circuit on a breadboard, and our explanation of what resistors do.

Questions

What are the seven basic logic gates?

AND, OR, NOT, NAND, NOR, XOR and XNOR. Some lists also include the buffer, which simply passes its input through unchanged.

Which gate is the universal gate?

Both NAND and NOR are universal gates: either one on its own can be used to build every other gate, and so any digital circuit.

What is the difference between OR and XOR?

With two inputs, OR gives 1 when one or both inputs are 1. XOR gives 1 only when the inputs are different, so 1 XOR 1 is 0.

What is a truth table?

A table with one row for every combination of a circuit’s inputs, showing the output for each. Tap any gate in the game to see its truth table, with the row it is using right now highlighted.

Does the game cost anything or need an account?

No. It is free, runs in your browser and needs no account. Your progress is saved in that browser on that device only, and the “Clear my progress” button in the Levels list removes it.

Sources

• Nexperia datasheets: 74HC00, 74HC02 (and its pin layout), 74HC04, 74HC08 (pins, the 2 V to 6 V supply range and the output current figures), 74HC32, 74HC86 and 74HC373.
• Texas Instruments: SN74HC7266 quadruple 2-input exclusive-NOR gates (datasheet listing), and Implications of slow or floating CMOS inputs.
• Philips: 74HC283 4-bit binary full adder with fast carry.
• Ken Shirriff: A computer built from NOR gates: inside the Apollo Guidance Computer.