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Introduction to Logic Gates
2026-08-31 | By Maker.io Staff
Digital electronics are everywhere, even if they often go unnoticed. They power many things, from a simple microwave to a highly integrated smartphone. At their core, they work with Boolean operations, and logic gates are the fundamental building blocks that implement these functions. Read on to learn all you need to know to get started with digital electronics and logic gates.
A Brief Introduction to Digital Electronics
Compared to analog circuits, which operate on continuous voltage levels, digital electronics reduce signals to two distinct, binary states: LOW and HIGH. A LOW level means that the voltage is below a certain threshold and is interpreted as zero volts. Conversely, a HIGH state indicates that the voltage on the line is above a defined threshold. Both states are equally valid signals, and a LOW state does not indicate the absence of a signal. Sometimes, it helps to think of these two states as FALSE for LOW and TRUE for HIGH.
The binary system is used in digital electronics because two-state signals serve as a more reliable way to represent information in noisy physical circuits. The abstracted signal is less likely to fluctuate enough to cause a change in state from HIGH to LOW or vice versa. This means that circuits, especially large systems, become more predictable and deterministic as a whole.
Binary values are also easy to distinguish reliably, and they allow circuits to make clear decisions based on electrical signals. For example, a transistor can be switched on or off using digital signals, and it can then control other parts of the circuit. These binary states can also be combined using Boolean operations to perform calculations, which is where logic gates come into play.
Understanding Basic Binary Operations
Logic functions operate on one or more binary values. The simplest useful logic function is NOT, also called inversion or negation. It simply flips the input state of one variable: LOW becomes HIGH, and HIGH becomes LOW. Alternatively speaking, NOT TRUE is FALSE, and NOT FALSE is TRUE.
The AND operation is one of the two simplest functions that combine the states of two or more variables. It outputs HIGH only when all inputs are HIGH. Similarly, the OR operation results in a HIGH state when any of its inputs is HIGH.
These are the three simplest logic functions. Importantly, NOT combined with either AND or OR is functionally complete, meaning any other logic function, no matter how complex, can be built using only two basic Boolean operations.
Lastly, it’s important to note that Boolean operators follow a defined order of evaluation. NOT is applied first, followed by AND, which takes precedence over OR, similar to how multiplication is evaluated before addition in standard arithmetic. You can also use parentheses to change the order.
This image illustrates the execution order of Boolean operations using a small example.
What Are Truth Tables?
A truth table is a systematic representation of all possible values of a logical expression. It simply lists all input variables and the result for each possible combination. It visually represents how changing certain inputs affects the output of a digital circuit. You can construct a truth table for every logic function you can think of, no matter how complicated or simple it is. For example, the truth table for the NOT function is as simple as it gets:
Remember that Boolean functions operate on binary values. A single binary variable can have one of two states: TRUE or FALSE. So each additional variable in a truth table adds another column and a multiple of two possible combinations. There are two combinations for one variable, four combinations for two variables, eight combinations for three variables, and so on. Generally speaking, a digital circuit with n variables can have two to the power of n different input combinations. For example, the truth table for a two-input AND function looks as follows:
As this example shows, truth tables are exhaustive, meaning that they list every possible input combination and how the circuit behaves for each of them. They are a complete, fully deterministic description of how digital circuits behave. Lastly, truth tables are often filled in with zeros for FALSE and ones for TRUE, just to make them more compact and faster to construct.
Using Truth Tables in Boolean Algebra
Truth tables can also help with Boolean algebra, as they can be used to hold intermediary results in more complex circuits. For example, take the following Boolean function that combines three operators:
y = NOT (a AND b OR c)
You can split this function into separate parts and assign the intermediate results to new variables. However, you must remember the execution order of the operations: NOT before AND before OR. Since the NOT is around parentheses, it is evaluated last in this formula:
d = a AND b
e = d OR c
y = NOT e
You can then construct an empty truth table with six columns and fill in all possible combinations of the original input variables:
Then, you simply need to fill in each decomposed column one after the other:
More Complex Standard Logic Functions
Simple Boolean functions can be combined into more complex blocks. For example, AND + NOT can be combined into a NAND gate, which is effectively an AND gate with its output inverted. Its truth table looks as follows:
The output of a NAND gate is HIGH as long as at least one of its inputs is LOW. The NOR gate is a similar composition of OR + NOT, and its output is HIGH when all its inputs are LOW:
Similar to how NOT combined with AND or OR is functionally complete, NAND or NOR alone is also functionally complete. This means that any logic function, no matter how complex, can be built using only NAND or only NOR gates. In practice, this led to NAND and NOR becoming the primary building blocks in digital electronics. Although this generally increases the number of gates needed for a circuit, it also means that manufacturers only need a single type of logic gate on the IC die. This simplification cuts production cost and can increase predictability, since all gates behave more uniformly.
The last of the more complex blocks is the XOR gate, and it represents the exclusive OR operation, meaning that its output is HIGH whenever exclusively one of its inputs is HIGH. For example, for two variables:
Logic Gates in the Real World
Logic gates are readily available in many different packages and with different numbers of inputs, making them easy to integrate into custom designs. One important family of logic gates for hobbyists is the 7400-series of integrated circuits. It encompasses all standard logic gates like AND, OR, NOT, XOR, and so on. It further contains many building blocks that combine several of these gates into more complex parts that are commonly found in digital circuits. Examples include memory blocks, decoders, and multiplexers.
Most of the standard logic gates in this series have the same or a very similar pinout, and they are often interchangeable should you need to swap out one logic function block for another. For example, all logic function ICs with two input variables combine four gates in one IC. The first two pins are the inputs to the first gate, and the third pin is the first gate’s output. The next two pins are the inputs to the next gate, followed by the second gate’s output. Pin seven is typically GND. The next six pins are two more independent gates, and pin 14 is usually the supply voltage pin:
This image shows the internals of a standard 7400 NAND gate. It has four independent NAND gates, each with two inputs. Image courtesy of ON semiconductor.
The standard NOT gate is a notable exception to this rule, since it only has a single input for each gate. Therefore, the standard 74x04 IC contains six independent gates in one package. In either case, it’s important to always check a manufacturer’s datasheet before adding a logic IC to a design, as it’s not guaranteed that they all follow the common pinout.
Lastly, it’s crucial to remember that real-world ICs have real-world limitations, most notably a maximum speed at which they can operate and certain delays, such as propagation delay. For example, propagation delay is the time for the chip’s output to become valid after the inputs are stable. Before that delay elapses, the output may not yet be valid, which can affect other parts of a larger circuit when not accounted for. Finally, adding small decoupling capacitors between the supply pins of each chip helps suppress noise and keep the chips stable.
Conclusion
Logic gates are the building blocks behind the binary logic used in digital circuits. Unlike analog circuits, which operate on continuous signals, digital circuits reduce everything to two defined states: LOW and HIGH. These two states make digital systems less susceptible to normal electrical fluctuations and easier to scale. Truth tables list every possible input combination and the resulting output, which helps a lot in understanding how larger logic circuits behave.
Simple Boolean operations such as NOT, AND, and OR define how binary inputs are processed and combined. Advanced gates such as NAND, NOR, and XOR are useful shortcuts that combine the simpler blocks. NAND and NOR are particularly important because either one alone is functionally complete, meaning any logic function can be built entirely using only gates of one type.
Logic gates are available as real integrated circuits, with the 7400-series being one of the most common series for hobbyists. These chips package multiple gates into a single IC and make it easy to prototype digital circuits using standard building blocks. However, real components still have physical limitations such as propagation delay, speed limits, and electrical noise.
