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

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.

If you would like to treat a binary signal as a discrete-time sequence having values of $$0$$s and $$1$$s, then you would plot them as all other discrete-time sequences, using the lollipop display.