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Mr. Pedantic on analog vs. digital, continuous vs. discrete

a guest May 29th, 2012 47 Never
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  1. Oh man, I hate to be Mr. Pedantic, and posting a week after this was discussed, but I'm coming late to this part of the class and I have issue with this position.  The difference between analog and digital is not the difference between discrete and continuous.
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  3. Continuous and discrete are *types of quantities*
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  5. * continuous: always another value between two values, ever finer differences possible
  6. * discrete: roughly "countable" (the integers); quantized
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  8. Analog and digital are *types of representation*
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  10. * analog: quantities are represented by analogous quantities
  11. * digital: quantities are represented by digits, quantity of digits does not directly correlate, the *kind* and *order* of digits is what is important
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  13. An unary number system (holding up fingers!) is discrete, but still analog: each raised finger represents one item.  Counting in binary on your fingers is discrete and digital, as each finger represents a binary digit, but it does not directly correspond to something counted, and it matters both when it is raised and lowered.  (and yes, I am aware that "digit" means "finger" originally)
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  15. As continuous quantities are necessarily represented via analogs, the two concepts have somewhat merged, but digital vs discrete is an important distinction.  It is the discrete aspect that provides noise resistance, the digital aspect makes a system much more *efficient*.
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  17. ----
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  19. As an amusing and possibly illustrative aside, while the ENIAC was mostly digital, it had a holdover from mechanical counting machines that made it partially analog.  An adding machine mechanism would have a wheel for each digit, marked so that its position indicates 0 through 9.  To add the two digits on wheel A and B and store the result in B, A would turn to a lower number (by 1) and simultaneously B to a higher number (by 1) until A gets to position 0.  If B turns from 9 to 0, then a mechanism turns the next higher digit in the number to do the carry.
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  21. The ENIAC was constructed the same way, but out of electrical counters.  Each counter was a ring of 10 electrical components, only one of which is active at a time, to represent a digit in a number.  There was a mechanism to add one to the count, switching to the next element in the ring.  A counter could transmit is value by counting down and emitting a pulse each time; like an old rotary phone, digits were transmitted throughout the machine as a series of pulses, and each pulse increments another counter by one. The same carry happens when going from element 9 to 0.  These counters were developed for counting faster than the mechanical equivalent, and found use in early electronic computing both for storing numbers and performing addition.
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  23. While using base ten requires fewer digits than base two (binary), each digit is far more complicated, and transmission of a pulse train is slow.  Several of ENIAC's predecessors and almost all of its successors used base two instead, where counting is reduced entirely to "one or nothing" within each digit, much more easily dealt with as a purely logical operation (in the Boolean sense).
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