# Why are binary signals drawn continuous in time despite being a digital signal [closed]

The conventional definiton of a Digital signal is as follows: A digital signal is a signal that is discrete in time and quantized in amplitude. Almost all resources (textbooks, online sources,etc) stick to this defintion and gives emphasis to the point that a digital signal is discrete in time.

A binary signal is a Digital signal.

But according to the defintion, the signal should be discrete in time to be a digital signal. In the plot, a binary signal is drawn as continuous in time. Then how can this be a digital signal according to the defintion.

A digital signal according to the definition should look like this:

Also I read that a digital signal has different meaning/definition in different contexts. For example the above mention definition is apt in the signal processing context, whereas in digital electronics where the binary signal mention above is used, a digital signal is a signal that takes only discrete amplitude values(ie. it is quantized in amplitude) and it can be continuous or discrete in time.

I am confused that why is the above definiton given a strict emphasis even in digital electronics context usually. Almost everywhere I look in internet and even some teachers give the conventional definition of a digital signal without mentioning the context.

Are my above findings correct? I would like to know the exact definitions of a digital signal according to different contexts.

• In reality, all signals are analog and vary continuously in both time and amplitude. Digital signals are obtained by chopping up an analog signal in both time and amplitude. – JRE Oct 6 '18 at 15:15
• But why is the binary signal despite being a digital signal represented as continous in time? – Justin Oct 6 '18 at 15:20
• Digital signals are often not discrete in time. They may have only two states, but they can change at any time. They maintain that state at all times between those changes, so drawing a discrete time diagram (like the one you have for what looks like a digitized signal) would be an absolute pain. – JRE Oct 6 '18 at 15:24
• So can we generalize and say that a digital signal is signal is a signal that is quantized in amplitude and it can be discrete or continuous in time? – Justin Oct 6 '18 at 15:26
• Here is a video on youtube that made many things click in my head. The video connects so many loose dots you've managed to gather while studying. – Harry Svensson Oct 6 '18 at 15:28

A digital representation of an analog quantity (having been captured in an ADC) is indeed discrete in time. I highly recommend The Scientist and Engineer's Guide to Digital Signal Processing for an excellent discussion of this, incidentally.

A physical signal between two or more points, such as in RS232, PCI express and many others that happen to take on a discrete number of states (in this case 2), is continuous in time, as are all physical layer signals.

The confusion is understandable.

One of my favourite quotes is:

There is no such thing as a digital signal: EMC testing proves this daily.

A note on digital signals; a perfect digital signal (0 rise and fall time) simply cannot exist as it would require infinite bandwidth.

• "a perfect digital signal (0 rise and fall time) simply cannot exist as it would require infinite bandwidth." ... Or, put another way, it would require either to be carried in a conductor with zero capacitance (meaning its conductor would need to be infinitely far from any other conductor) or to be driven by a source circuit that could supply infinite current (so that the capacitances that do exist will be fully charged instantaneously). – Jules Oct 6 '18 at 21:53
• "a perfect digital signal (0 rise and fall time) simply cannot exist as it would require infinite bandwidth."Can you please elaborate why would this require infinite bandwidth? – Justin Oct 7 '18 at 11:08

I can't quite make out where your confusion is but perhaps the following will help.

A digital signal is a signal that is discrete in time and quantized in amplitude.

I think that all we're saying here is that the digital signal has some fixed value for a period of time. In your example that's the sample time.

A binary signal is a Digital signal.

True (but with a small 'd' as 'digital' is not a proper noun).

A binary signal, also known as a logic signal, is a digital signal with two distinguishable levels.

Agreed.

But according to the definition, the signal should be discrete in time to be a digital signal. In the plot, a binary signal is drawn as continuous in time. Then how can this be a digital signal according to the definition.

Figure 1. OP's graphic with quantized overlay.

The grey trace in your diagram is the analog signal that is being digitized. The red vertical bars are the result of the analog to digital conversion (ADC). I have superimposed the blue trace which shows what has been stored and what would be produced by a digital to analog conversion (DAC) if you were to play back the stored samples at the same rate that they were recorded. Obviously, this is not a high-fidelity reproduction of the original signal but it could be improved quite a bit with low-pass filtering.

Does that help?