Logic level

Key takeaways

Logic level belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Logic level to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Logic level from memory before moving on to harder problems.

Reference excerpt

In digital circuits, a logic level is one of a finite number of states that a digital signal can inhabit. Logic levels are usually represented by the voltage 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 numbers 1 and 0 respectively or truth values true and false respectively. Signals with one of these two levels can be used in Boolean algebra 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).

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 (Q) 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 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 resistors 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. 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 Karnaugh map § Don't cares).

9-level logic IEEE 1164 defines 9 logic states for use in electronic design automation. 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 codes may use more than two states to encode and transmit data more efficiently. Examples include alternate mark inversion 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 ) Simple MOSFET-based logic level conversion or level-shift based on work done by Herman Schutte at Philips Semiconductors Systems Laboratory in Eindhoven

Worked examples

Example 1 — a first encounter with Logic level

Start with the simplest possible case. Write down what Logic level claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Logic level before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Logic level ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Logic level

In research: Logic level appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Logic level in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Logic level is common in secondary-school and first-year university syllabi. It links to neighbouring topics Digital electronics, so understanding it makes those chapters shorter.
In everyday life: Look for Logic level outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Logic level in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Logic level means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Logic level out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Logic level in simple terms?

In digital circuits, a logic level is one of a finite number of states that a digital signal can inhabit. Logic levels are usually represented by the voltage difference between the signal and ground, although other standards exist.

Why does Logic level matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Logic level?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Logic level.