what amazes me is that 15 years ago my family had a computer with 2MB of total disk space. today, i can fit 2000 times that on a device smaller than my thumb.
That is something different. You didn't translate the number eleven into binary, you translated the text "11". Here you have two characters, each displayed as "1". In the ASCII code (and in many other codes), the code for digits "0" to "9" are 48 to 57 (letters "A" to "Z" are 65 to 90, "a" to "z" are 97 to 122 and so on). So "11" is twice the code 49. And 49 in binary is 00110001.
Yeah, it gets really fun when you get into signed arithmetic and finally realize that if you create a binary adder that works then signed and unsigned arithmetic both work without modification (provided you're using standard 2s compliment notation) and know whether or not the numbers are supposed to be signed. I've had to convince my coworkers on multiple occasions that a counter that had no knowledge of sign worked in both directions if the increment value was set as positive or negative since it's all a matter of interpretation of the results.
I've always been a person that has preferred the lowest level I can get to for programming, luckily right now I program logic devices so I'm at the bit manipulation stage, if I have to move up hopefully I can get to play with Assembly language, especially once you start playing with processor simulators and pipelining to make sure as many operational units on a processor are active every clock cycle.