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In the real world, electrical signals are analog (including digital ones!). An oscilloscope allows you to view analog voltages and how they change over time. Oscilloscopes are best used for evaluating signal integrity and measuring analog circuit performance.
On the other hand, Logic analyzers represent signals in their digital form: a logic 0 or logic 1. This is similar to an oscilloscope with a 1-bit resolution. However, most logic analyzers have many more channels than oscilloscopes (8, 16, or even over 100 channels). Logic analyzers are great tools for viewing digital waveforms, debugging digital communication (e.g. Serial, I2C), and characterizing digital systems with many lines (e.g. FPGAs).
Uses
Choosing the right tool for the job can be a crucial step when debugging circuits. At its core, an oscilloscope is useful for measuring and visualizing analog signals with 1-4 channels. A logic analyzer is best for digital systems with more than 4 channels.
An oscilloscope can help you visualize analog waveforms and measure various characteristics, such as amplitude, ringing, transient signals, phase and unwanted pulses. Even when debugging digital systems, you can easily measure signal integrity with an oscilloscope.

Example of an oscilloscope displaying a sine wave and overshoot on two channels
However, if you need to monitor and debug the output of a digital system or capture digital communication, such as serial and I2C, a logic analyzer is often the better tool. Logic analyzers generally offer more channels than an oscilloscope and can display data in state mode, where one of the channels acts as a clock.

Example of a logic analyzer displaying digital signals on six channels
Differences
The differences between oscilloscopes and logic analyzers can be summarized in the following table:
| Oscilloscope | Logic Analyzer |
| Measure and display analog signals on a few channels | Measure and display digital signals on many channels |
| Repeatedly store and display small snapshots | Record data before displaying |
| Displays signals in real time | Allows users to navigate potentially long recordings |
| Measure amplitude and timing of a waveform | Measure time between data capture points |
| Offers real-time features, like fast Fourier transform (FFT) | Offers features unique to digital systems, like protocol analyzers |
| Simple threshold or pulse-width triggers used to show a steady waveform | Complex triggering system used to capture and filter data |
How Do Oscilloscopes Work?
The following diagram shows the basic functional blocks that can be found in a digital storage oscilloscope (DSO). Note that some blocks have been left out for the sake of simplicity.

Block diagram of an oscilloscope
How Do Logic Analyzers Work?
The following diagram shows the basic functional blocks found in most logic analyzers. Like in the oscilloscope example, the blocks have been simplified.

Block diagram of a logic analyzer
Mixed Signal Oscilloscope
Sometimes, you might find yourself in need of both a logic analyzer and an oscilloscope. Many electrical engineers will have both machines on their workbench. However, the combination of logic analyzer and oscilloscope can be found in a piece of equipment called the Mixed Signal Oscilloscope (MSO).

Example of a Mixed Signal Oscilloscope
Image credits: " 350 MHz Mixed Signal Oscilloscope HMO3524 by HAMEG Instruments" by Hameg is licensed under CC BY SA 3.0
MSOs can capture and display analog as well as digital signals. They often have several oscilloscope channels along with dozens of digital inputs. Additionally, they can be configured with complex triggers based on both analog and digital characteristics.
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