Is bit-shifting mathematically meaningful?

I mean in the sense that it can be related to the real world somehow. For example, 80/2 can be represented by a baker making eighty pies, and Lex Luthor stealing half of them. From the real world to math, I can measure the velocity of an object over time, graph that, say the equation *f*(x) represents the line of that graph, then calculate the integral of *f*(x) and say it represents the acceleration of the original object over time.

Bit-shifting, however... to express a number in binary, then 'move' the bits like so:

00100000 >> 2 = 00001000

I don't know how that can be related to the real world. Is this something that only has meaning in symbolic logic?

digit shifting is like multiplying by the radix of the number.