Logic Gates

A logic gate is an electronic circuit that operates on digital signals -- it is the basic building block of essentially every digital system, taking one or more binary inputs and producing a single binary output. There are three BASIC logic gates -- AND, OR and NOT -- and three DERIVED gates built from combinations of the basic ones -- NAND, NOR and Ex-OR -- each covered in its own sub-section below, always with its circuit symbol, its truth table (the exhaustive lis …

The two-input AND gate has inputs A and B and output Y, related by the Boolean equation $Y=A\cdot B$ -- this '.' operator performs LOGICAL multiplication, distinct from ordinary arithmetic multiplication even though it is written and often computed the same way for single bits. Its logic operation: the output is HIGH (logic 1) only when ALL the inputs are high; for every other input combination the output is LOW (logic 0). Concretely, the truth table gives $Y=0$ for $(A,B)=(0,0),(0,1),(1,0)$ and $Y=1$ only for $(A,B)=(1,1)$. …

The two-input OR gate has inputs A and B and output Y, related by the Boolean equation $Y=A+B$ -- this '+' operator performs LOGICAL addition, distinct from ordinary arithmetic addition (in particular $1+1=1$ in Boolean algebra, not 2). Its logic operation: the output is HIGH (logic 1) when EITHER input, or both, are high; the output is LOW only when both inputs are low. Concretely, the truth table give …

The single-input NOT gate has input A and output Y, related by the Boolean equation $Y=\overline{A}$ -- the overbar denotes logical COMPLEMENT (also called inversion or negation). Its logic operation: the output is simply the complement of the input, which is why a NOT gate is also called an inverter -- when A is 0, Y is 1, and when A is 1, Y is 0. It is the only basic gate with a single input. Because it has only one input, the NOT gate's truth table has just two rows rather than the four every other gate in this section needs, and it is the only basic gate whose Boolean equation uses the overbar complement symbol on a single variable rather than combining two variables with '+' or '.'. It is also the gate directly realised by a single common-emitter transistor switch stage (9 …

The two-input NAND gate ('NOT-AND') has inputs A and B and output Y, related by the Boolean equation $Y=\overline{A\cdot B}$ -- literally an AND gate followed by a NOT gate, and its output is exactly the COMPLEMENT of what an ordinary AND gate would give for the same inputs. Its logic operation: the output is LOW (logic 0) only when ALL inputs are high (the one case where a plain AND would have gi …

The two-input NOR gate ('NOT-OR') has inputs A and B and output Y, related by the Boolean equation $Y=\overline{A+B}$ -- literally an OR gate followed by a NOT gate, its output the exact COMPLEMENT of what an ordinary OR gate would give for the same inputs. Its logic operation: the output is HIGH (logic 1) only when ALL inputs are LOW (the one case where a plain OR would have give …

The two-input Ex-OR (exclusive-OR) gate has inputs A and B and output Y, related by the Boolean equation $Y=A\oplus B=A\overline{B}+\overline{A}B$ -- the $\oplus$ symbol denotes the Ex-OR operation directly, and the expanded form shows it can also be built from two AND gates (one taking A and $\overline{B}$, the other taking $\overline{A}$ and B) feeding a final OR gate. Its logic operation: the output is HIGH (logic 1) only when the two inputs DIFFER (exactly one of the two is high); when both inputs are the same (both 0 or both 1) the output is LOW. For an Ex-OR gate extended to MORE than two inputs, the output is high whenever an ODD number of inputs are high. …