Logic gates explained simply: AND, OR, NOT and XOR
A logic gate takes in 0s and 1s and gives back a single 0 or 1, always following the same rule. Four rules are enough to get started. For each one: an everyday example, its symbol, its truth table and a free circuit to play on the site.
First of all: 0 and 1
In digital electronics, a wire has only two states: low voltage (0) or high voltage (1). You can also read 0 as “false” and 1 as “true”. A logic gate takes one or two of these signals as inputs and produces a single output. In the diagrams below, A and B are the inputs and the lamp stands for the output: on for 1, off for 0. Next to each diagram, the truth table gives the output S (our label, from the French sortie) for every possible combination of inputs.
AND: everything has to be true
The AND gate outputs 1 only when all its inputs are 1. A washing machine only starts if the door is shut AND you have pressed “Start”. With the door open, nothing happens, however hard you press. A card payment goes through if the PIN is right AND there is enough money in the account.
| A | B | S |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The symbol is D-shaped: the inputs come in on the flat side and the output leaves from the rounded side. Try it: “The double lock”, the circuit on the AND gate page, can be played straight away, with no sign-up.
OR: one is enough
The OR gate outputs 1 as soon as at least one input is 1. A car's interior light comes on if the driver's door OR the passenger's door is open; if both are open, it stays on. That's the catch: in everyday speech, “or” often means “one or the other, but not both”. In logic, OR is happy with both.
| A | B | S |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
The symbol looks like an arrowhead with curved sides, curved inward on the input side. Try it: “The alarm”, on the OR gate page.
NOT: the opposite
The NOT gate (or inverter) has a single input and gives back the opposite: 0 becomes 1, 1 becomes 0. A car's seatbelt warning light works this way: it comes on when the belt is NOT fastened. In programming, it's the “not” in “if the file does not exist”, a test that comes up everywhere.
| A | S |
|---|---|
| 0 | 1 |
| 1 | 0 |
The symbol is a triangle followed by a small circle. The circle means “inverted”, and you'll see it on other gates too. Try it: “The key and the alarm”, on the NOT gate page, which pairs it with an AND.
XOR: one or the other, not both
The XOR gate (exclusive OR) outputs 1 when its two inputs are different. The classic example is a staircase light with one switch at the bottom and one at the top: flip either one and the lamp changes state. Another one: two pupils answer a true-or-false question, and the teacher wants to spot the papers where they disagree. XOR is also how computers add: the sum of two bits, leaving out the carry, is exactly an XOR.
| A | B | S |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The symbol is the OR shape with a second curved line in front of the inputs. Try it: “The two-way switch”, on the XOR gate page.
What next?
These four gates can be chained: the output of one becomes the input of the next. That is how you get circuits that take a majority vote or add numbers. The 10 free circuits on our home page take you along that path: they open one after the other, bring in one gate at a time, then combine them up to a half adder. Two more gates, NAND and NOR, are simply an AND and an OR followed by an inverter; they have their own page.