Digital - Analog

"However, the claim that Bitcoin is anonymous is a myth. The block chain is public, meaning that it’s possible for anyone to see every Bitcoin transaction ever. Although Bitcoin addresses aren’t immediately associated to real-world identities, computer scientists have done a great deal of work figuring out how to de-anonymize “anonymous” social networks. The block chain is a marvellous target for these techniques. I will be extremely surprised if the great majority of Bitcoin users are not identified with relatively high confidence and ease in the near future. The confidence won’t be high enough to achieve convictions, but will be high enough to identify likely targets. Furthermore, identification will be retrospective, meaning that someone who bought drugs on Silk Road in 2011 will still be identifiable on the basis of the block chain in, say, 2020. These de-anonymization techniques are well known to computer scientists, and, one presumes, therefore to the NSA. I would not be at all surprised if the NSA and other agencies have already de-anonymized many users. It is, in fact, ironic that Bitcoin is often touted as anonymous. It’s not. Bitcoin is, instead, perhaps the most open and transparent financial instrument the world has ever seen. ... What is, I believe, much more interesting and enjoyable is to think of Bitcoin and other cryptocurrencies as a way of enabling new forms of collective behaviour."

http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-actually-works/

"We show that the analog implementation requires 5 times less area, and consumes 20 times less energy than the digital design. As a result, the analog neuron, in spite of its greater design complexity, is a serious contender for future large-scale silicon neural systems."

http://pages.saclay.inria.fr/olivier.temam/files/eval/JBTH12.pdf

"Analogue systems invariably include noise; that is, random disturbances or variations, some caused by the random thermal vibrations of atomic particles. Since all variations of an analogue signal are significant, any disturbance is equivalent to a change in the original signal and so appears as noise.5 As the signal is copied and re-copied, or transmitted over long distances, these random variations become more significant and lead to signal degradation. Other sources of noise may include external electrical signals or poorly designed components. These disturbances are reduced by shielding, and using low-noise amplifiers (LNA).6

Analogue vs. digital electronics

Since the information is encoded differently in analogue and digital electronics, the way they process a signal is consequently different. All operations that can be performed on an analogue signal such as amplification, filtering, limiting, and others, can also be duplicated in the digital domain. Every digital circuit is also an analogue circuit, in that the behaviour of any digital circuit can be explained using the rules of analogue circuits.

The first electronic devices invented and mass produced were analogue. The use of microelectronics has made digital devices cheap and widely available.

Noise

Because of the way information is encoded in analogue circuits, they are much more susceptible to noise than digital circuits, since a small change in the signal can represent a significant change in the information present in the signal and can cause the information present to be lost. Since digital signals take on one of only two different values, a disturbance would have to be about one-half the magnitude of the digital signal to cause an error; this property of digital circuits can be exploited to make signal processing noise-resistant. In digital electronics, because the information is quantized, as long as the signal stays inside a range of values, it represents the same information. Digital circuits use this principle to regenerate the signal at each logic gate, lessening or removing noise.7"

http://en.wikipedia.org/wiki/Analogue_electronics

"Going even deeper, there is no such thing as a purely digital signal. When expressed in terms of voltage, a one might be 5V and a zero, 0V. But no actual circuit can make an instantaneous transition from 0 to 5V or back. There’s always some small amount of time where the voltage is rising or falling. In really high-speed circuits or over longer distances, a signal can be both a one and a zero at different points on the wire. This is what engineers mean when they say a circuit has to be modeled as a transmission line. So even digital circuits are actually analog underneath. Digital is really just another way of imposing meaning on an analog circuit."

http://rdist.root.org/2010/03/12/why-digital-logic-is-different-than-analog/

"We’d still be using analog computers today if it wasn’t for noise. The same advantages to working with a continuous analog signal mean it is vulnerable to cascading noise. On every pass through an op-amp, a small amount of noise is added. At some point, the signal is not recoverable from the noise and the calculation can’t proceed. Much of the more recent work on analog computers seems to be focused on filtering noise.

"As we saw last time, there is no such thing as a purely digital computer. “Digital” is a point-of-view, a way of interpreting an analog signal of some kind. This is both simple and sublime. It means that we can overcome the [dis]advantages inherent in our analog world by moving up a level of abstraction — manipulating symbols and abstract logic instead of concrete and continuous substances such as a voltage.

"Digital logic was designed to have the regenerative property. What this means is that each stage of processing starts over from scratch, generating its own signal that was only dependent on the meaning of the previous stages of logic and its computational result. The key thing to understand here is that it is not amplifying the input signal directly, it is regenerating the output by switching a set of transistors. This means that digital logic stages can be infinitely deep and the signal at the end is as free of noise as it was at the start."

http://rdist.root.org/2010/03/18/why-digital-logic-is-different-than-analog-part-2/