How much is modern programming still tied to underyling digital logic? [closed]

Question

First of all: I've got no academic background. I'm working primarily with Java and Spring and I'm also fond of web programming and relational databases. I hope I'm using the right terms and I hope that this vague question makes some sense.

Today the following question came to my mind: How much is modern programming still tied to the underlying digital logic? With modern programming I mean concepts like OOP, AOP, Java 7, AJAX, … I hope you get the idea.

Do they no longer need the digital logic with which computers are working internally? Or is binary logic still ubiquitous when programming this way? If I'd change the inner workings of a computer overnight, would it matter, because my programming techniques are already that abstract?

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P. S.: With digital logic I mean the physical representation of everything "inside" the computer as zeroes and ones.

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Changed "binary" to "digital".