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In
digital circuit In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematica ...
s, a logic level is one of a finite number of states that a
digital signal A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; ...
can inhabit. Logic levels are usually represented by the
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
difference between the signal and ground, although other standards exist. The range of voltage levels that represent each state depends on the logic family being used. A '' logic-level shifter'' can be used to allow compatibility between different circuits.


2-level logic

In binary logic the two levels are logical high and logical low, which generally correspond to
binary number A binary number is a number expressed in the Radix, base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A ''binary number'' may ...
s 1 and 0 respectively or
truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in ...
s ''true'' and ''false'' respectively. Signals with one of these two levels can be used in
Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denot ...
for digital circuit design or analysis.


Active state

The use of either the higher or the lower voltage level to represent either logic state is arbitrary. The two options are active high (''positive logic'') and active low (''negative logic''). Active-high and active-low states can be mixed at will: for example, a read only memory integrated circuit may have a chip-select signal that is active-low, but the data and address bits are conventionally active-high. Occasionally a logic design is simplified by inverting the choice of active level (see
De Morgan's laws In propositional calculus, propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both Validity (logic), valid rule of inference, rules of inference. They are nam ...
). The name of an active-low signal is historically written with a bar above it to distinguish it from an active-high signal. For example, the name Q, read ''Q bar'' or ''Q not'', represents an active-low signal. The conventions commonly used are: * a bar above () * a leading slash (/Q) * a leading exclamation mark (!Q) * a lower-case ''n'' prefix or suffix (nQ, Qn or Q_n) * an upper-case ''N'' suffix (Q_N) * a trailing # (Q#), or * an _B or _L suffix (Q_B or Q_L). Many control signals in electronics are active-low signals (usually reset lines, chip-select lines and so on). Logic families such as TTL can sink more current than they can source, so fanout and noise immunity increase. It also allows for wired-OR logic if the logic gates are open-collector/ open-drain with a pull-up resistor. Examples of this are the I²C bus, CAN bus, and PCI bus. Some signals have a meaning in both states and notation may indicate such. For example, it is common to have a read/write line designated R/W, indicating that the signal is high in case of a read and low in case of a write.


Logic voltage levels

The two logical states are usually represented by two different voltages, but two different currents are used in some logic signaling, like digital current loop interface and current-mode logic. High and low thresholds are specified for each logic family. When below the low threshold, the signal is ''low''. When above the high threshold, the signal is ''high''. Intermediate levels are undefined, resulting in highly implementation-specific circuit behavior. It is usual to allow some tolerance in the voltage levels used; for example, 0 to 2 volts might represent logic 0, and 3 to 5 volts logic 1. A voltage of 2 to 3 volts would be invalid and occur only in a fault condition or during a logic-level transition. However, few logic circuits can detect such a condition, and most devices will interpret the signal simply as high or low in an undefined or device-specific manner. Some logic devices incorporate
Schmitt trigger In electronics, a Schmitt trigger is a comparator circuit with hysteresis implemented by applying positive feedback to the noninverting input of a comparator or differential amplifier. It is an passivity (engineering), active circuit which con ...
inputs, whose behavior is much better defined in the threshold region and have increased resilience to small variations in the input voltage. The problem of the circuit designer is to avoid circumstances that produce intermediate levels, so that the circuit behaves predictably. Nearly all digital circuits use a consistent logic level for all internal signals. That level, however, varies from one system to another. Interconnecting any two logic families often required special techniques such as additional
pull-up resistor In electronic logic circuits, a pull-up resistor (PU) or pull-down resistor (PD) is a resistor used to ensure a known state for a signal. More specifically, a pull-up resistor or pull-down resistor ensures that a wire will have a high logic lev ...
s or purpose-built interface circuits known as level shifters. A level shifter connects one digital circuit that uses one logic level to another digital circuit that uses another logic level. Often two level shifters are used, one at each system: A line driver converts from internal logic levels to standard interface line levels; a line receiver converts from interface levels to internal voltage levels. For example, TTL levels are different from those of
CMOS Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss ", , ) is a type of MOSFET, metal–oxide–semiconductor field-effect transistor (MOSFET) semiconductor device fabrication, fabrication process that uses complementary an ...
. Generally, a TTL output does not rise high enough to be reliably recognized as a logic 1 by a CMOS input, especially if it is only connected to a high-input-impedance CMOS input that does not source significant current. This problem was solved by the invention of the 74HCT family of devices that uses CMOS technology but TTL input logic levels. These devices only work with a 5 V power supply.


More than two levels


3-value logic

Though rare, ternary computers evaluate base 3 three-valued or ternary logic using 3 voltage levels.


3-state logic

In three-state logic, an output device can be in one of three possible states: 0, 1, or Z, with the last meaning high impedance. This is not a voltage or logic level, but means that the output is not controlling the state of the connected circuit.


4-value logic

Four valued logic adds a fourth state, X (''don't care''), meaning the value of the signal is unimportant and undefined. It means that an input is undefined, or an output signal may be chosen for implementation convenience (see ).


9-level logic

IEEE 1164 defines 9 logic states for use in
electronic design automation Electronic design automation (EDA), also referred to as electronic computer-aided design (ECAD), is a category of software tools for designing Electronics, electronic systems such as integrated circuits and printed circuit boards. The tools wo ...
. The standard includes strong and weakly driven signals, high impedance and unknown and uninitialized states.


Multi-level cells

In solid-state storage devices, a multi-level cell stores data using multiple voltages. Storing n bits in one cell requires the device to reliably distinguish 2n distinct voltage levels.


Line coding

Digital
line code In telecommunications, a line code is a pattern of voltage, current, or photons used to represent digital data transmission (telecommunications), transmitted down a communication channel or written to a storage medium. This repertoire of signal ...
s may use more than two states to encode and transmit data more efficiently. Examples include
alternate mark inversion In telecommunication, bipolar encoding is a type of return-to-zero (RZ) line code, where two nonzero values are used, so that the three values are +, −, and zero. Such a signal is called a duobinary signal. Standard bipolar encodings are designed ...
and 4B3T from telecommunications, and pulse-amplitude modulation variants used by Ethernet over twisted pair. For instance, 100BASE-TX uses MLT-3 encoding with three differential voltage levels (−1V, 0V, +1V) while 1000BASE-T encodes data using five differential voltage levels (−1V, −0.5V, 0V, +0.5V, +1V). Once received, the line coding is converted back to binary.


See also

* Logic family * Digital current loop interface


References


External links


Positive Logic (active-high) and Negative logic (active-low )
{{DEFAULTSORT:Logic Level Digital electronics