All logic circuits may be described in terms of three fundamental elements, shown graphically in the illustration. The NOT element has one input and one output; as the name suggests, the output generated is the opposite of the input in binary. In other words, a 0 input value causes a 1 to appear at the output; a 1 input results in a 0 output. (All signals are interpreted to be one of only two values, denoted as 0 and 1.)

Logic elements.

The AND element has an arbitrary number of inputs and a single output. As the name suggests,the output becomes 1 if, and only if, all of the inputs are 1; otherwise the output is 0. The AND together with the NOT circuit therefore enables searching for a particular combination of binary signals.

The third element is the OR function. As with the AND, an arbitrary number of inputs may exist and one output is generated. The OR output is 1 if one or more inputs are 1.

The operations of AND and OR have some analogies to the arithmetic operations of multiplication and addition, respectively. The collection of mathematical rules and properties of these operations is called boolean algebra.

While the NOT, AND, and OR functions have been designed as individual circuits in many circuit families, by far the most common functions realized as individual circuits are the NAND and NOR circuits of the illustration. A NAND may be described as equivalent to an AND element driving a NOT element. Similarly, a NOR is equivalent to an OR element driving a NOT element.

As the names of the logic elements described suggest, logic circuits respond to combinations of input signals. Logic networks which are interconnected so that the current set of output signals is responsive only to the current set of input signals are appropriately termed combinational logic.

An important further capability for processing information is memory, or the ability to store information. The logic circuits themselves must provide a memory function if information is to be manipulated at the speeds the logic is capable of. Logic circuit networks that include feedback paths to retain information are termed sequential logic networks, since outputs are in part dependent on the prior input signals applied and in particular on the sequence in which the signals were applied.

Several alternatives exist for the digital designer to create a digital system. Two common realizations are ready-made catalog-order devices, which can be combined as building blocks, and custom-designed devices. Gate-array devices comprise a two-dimensional array of logic cells, each equivalent to one or a few logic gates. Programmable logic arrays have the potential for realizing any of a large number of different sets of logic functions. In table look-up, the collection of input signals are grouped arbitrarily as address digits to a memory device. Finally, the last form of logic network embodiment is the microcomputer.

**logic circuit**, electric circuit whose output depends upon the input in a way that can be expressed as a function in symbolic logic; it has one or more binary inputs (capable of assuming either of two states, e.g., “on” or “off”) and a single binary output. Logic circuits that perform particular functions are called gates. Basic logic circuits include the AND gate, the OR gate, and the NOT gate, which perform the logical functions AND, OR, and NOT. Logic circuits can be built from any binary electric or electronic devices, including switches, relays, electron tubes, solid-state diodes, and transistors; the choice depends upon the application and design requirements. Modern technology has produced integrated logic circuits, modules that perform complex logical functions. A major use of logic circuits is in electronic digital computers. Fluid logic circuits have been developed whose function depends on the flow of a liquid or gas rather than on an electric current.

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