INPUT | OUTPUT | |
---|---|---|

A | B | A AND B |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

The **AND gate** is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If none or not all inputs to the AND gate are HIGH, a LOW output results. The function can be extended to any number of inputs.

There are three symbols for AND gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN symbol. Additional inputs can be added as needed. For more information see Logic Gate Symbols. It can also be denoted as symbol "^" or "&".

MIL/ANSI Symbol | IEC Symbol | DIN Symbol |

The AND gate with inputs *A* and *B* and output *C* implements the logical expression . This expression also may be denoted as **C=A^B** or **C=A&B**.

An AND gate is usually designed using N-channel (pictured) or P-channel MOSFETs. The digital inputs **a** and **b** cause the output **F** to have the same result as the AND function.

is the analytical representation of AND gate:

If no specific AND gates are available, one can be made from NAND or NOR gates, because NAND and NOR gates are "universal gates," ^{ [1] } meaning that they can be used to make all the others.

Desired gate | NAND construction | NOR construction |
---|---|---|

AND gates are available in IC packages. The 7408 IC is a well known QUAD 2-Input AND GATES and contains four independent gates each of which performs the logic AND function.

Wikimedia Commons has media related to . AND gates |

In logic, a **logical connective** is a symbol or word used to connect two or more sentences in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.

A **logic gate** is an idealized or physical electronic device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an **ideal logic gate**, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device.

In Boolean functions and propositional calculus, the **Sheffer stroke** denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called **nand** or the **alternative denial**, since it says in effect that at least one of its operands is false. In digital electronics, it corresponds to the NAND gate. It is named after Henry M. Sheffer and written as ↑ or as |. In Bocheński notation it can be written as D*pq*.

In digital logic, an **inverter** or **NOT gate** is a logic gate which implements logical negation. The truth table is shown on the right.

**Exclusive or** or **exclusive disjunction** is a logical operation that outputs true only when inputs differ.

The method of **logical effort**, a term coined by Ivan Sutherland and Bob Sproull in 1991, is a straightforward technique used to estimate delay in a CMOS circuit. Used properly, it can aid in selection of gates for a given function and sizing gates to achieve the minimum delay possible for a circuit.

In logic, a **truth function** is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values. The typical example is in propositional logic, wherein a compound statement is constructed by one or two statements connected by a logical connective; if the truth value of the compound statement is determined by the truth value(s) of the constituent statement(s), the compound statement is called a **truth function**, and the logical connective is said to be **truth functional**.

In Boolean algebra, any Boolean function can be put into the **canonical disjunctive normal form** (**CDNF**) or **minterm canonical form** and its dual **canonical conjunctive normal form** (**CCNF**) or **maxterm canonical form**. Other canonical forms include the complete sum of prime implicants or Blake canonical form, and the algebraic normal form.

The **OR gate** is a digital logic gate that implements logical disjunction – it behaves according to the truth table to the right. A HIGH output (1) results if one or both the inputs to the gate are HIGH (1). If neither input is high, a LOW output (0) results. In another sense, the function of OR effectively finds the *maximum* between two binary digits, just as the complementary AND function finds the *minimum*.

In digital electronics, a **NAND gate** (**NOT-AND**) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan's theorem, a two-input NAND gate's logic may be expressed as AB=A+B, making a NAND gate equivalent to inverters followed by an OR gate.

**XOR gate** is a digital logic gate that gives a true output when the number of true inputs is odd. An XOR gate implements an exclusive or; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both".

The NAND Boolean function has the property of functional completeness. This means, any Boolean expression can be re-expressed by an equivalent expression utilizing *only* NAND operations. For example, the function NOT(x) may be equivalently expressed as NAND(x,x). In the field of digital electronic circuits, this implies that we can implement any Boolean function using just NAND gates.

The **XNOR gate** is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.

The **NOR gate** is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator. It can also in some senses be seen as the inverse of an AND gate. NOR is a functionally complete operation—NOR gates can be combined to generate any other logical function. It shares this property with the NAND gate. By contrast, the OR operator is *monotonic* as it can only change LOW to HIGH but not vice versa.

**Diode logic** (DL), or **diode-resistor logic** (DRL), is the construction of Boolean logic gates from diodes. Diode logic was used extensively in the construction of early computers, where semiconductor diodes could replace bulky and costly active vacuum tube elements. The most common use for diode logic is in diode–transistor logic (DTL) integrated circuits that, in addition to diodes, include inverter logic for power gain and signal restoration.

In logic, a **functionally complete** set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is { AND, NOT }, consisting of binary conjunction and negation. Each of the singleton sets { NAND } and { NOR } is functionally complete.

**AND-OR-Invert** (AOI) logic and AOI gates are two-level compound logic functions constructed from the combination of one or more AND gates followed by a NOR gate. Construction of AOI cells is particularly efficient using CMOS technology where the total number of transistor gates can be compared to the same construction using NAND logic or NOR logic. The complement of AOI Logic is OR-AND-Invert (OAI) logic where the OR gates precede a NAND gate.

A **truth table** is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.

In electronics, a **flip-flop** or **latch** is a circuit that has two stable states and can be used to store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems.

- ↑ Mano, M. Morris and Charles R. Kime.
*Logic and Computer Design Fundamentals, Third Edition.*Prentice Hall, 2004. p. 73.

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