In a figure when the explicit value of a sink output

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Unformatted text preview: ter implements the Fredkin gate: DExercise 3.30: Verify that the billiard ball computer in Figure 3.14 computes the Sources Fredkin gate. Bennett, C. H. The Thermodynamics of Computation — a Review. Int. J. In addition to reversibility, the Fredkin gate also has the interesting property that Theo. Phys., 21, 12 (1982), 905–940. the number of 1s is conserved between the input and output. In terms of the billiard ball computer, this corresponds to the number of billiard balls going into the Fredkin gate being equal to the number coming out. Thus, it is sometimes referred to as being a conservative reversible logic gate. Such reversibility and conservative properties are interesting to a physicist because they can be motivated by fundamental physical princi- 66 CHAPTER II. PHYSICS OF COMPUTATION Figure 8 Realization of the J-K flip-flop. ¯ Figure II.26: Implementation of J-K flip-flop. [from FT82] Finally, Figure 8 shows a conservative-logic realization of the J-¬K flip-flop. (In a figure, when the explicit value of a sink output is irrelevant to the discussion we shall generically represent this value by a question mark.) Unlike the previous circuit, where the wires Petrosyan, Artyom, Ciliberto,a Sergio, network Berut, Antoine, Arakelyan, Artak, act as "transmission" lines, this is sequential with feedback, and the wire plays an effective role as a "storage" element. Dillenschneider, Raoul and Lutz, Eric. Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 4. COMPUTATION UNIVERSALITYdoi:10.1038/nature10872 LOGIC OF CONSERVATIVE 483, 187–189 (08 March 2012). An important result of conservative logic is that it is possible to preserve the computing capabilities of Frank, Michael satisfying the "physical" constraints of reversibility and conservation. ordinary digital logic while P. Introduction to Reversible Computing: Motivation, Progress, and Challenges. CF ‘05, May 4–6, 2005, Ischia, Italy. Let us consider an arbitrary sequential network constructed out of conventional logic elements, such as AND and OR gates, inverters F., "NOT" gates), FAN-OUT nodes, and delay elements. For ,definiteness, we shall Fredkin, E. (or To↵oli, T. Conservative logic. Int. J. Theo. Phys. 21, 3/4 use as an example the network of Figure 9-a serial adder (mod 2). By replacing in a one-to-one fashion these (1982), 219–253. elements (with the exception of the delay element-cf. footnote at the end of Section 3) with a conservativelogic realization of the same elements (as given, for example, in Figures 4b, 6a, 6b, and 6c), one obtains a conservative-logic network that performs the same computation (Figure 10). Such a realization may involve a nominal slow-down factor, since a path that in the original network contained only one delay element may now traverse several unit wires. (For instance, the realization of Figure 9 has a slow-down factor of 5; note, however, that only every fifth time slot is actually used for the given computation, and the remaining four time slots are available for other independent computations, in a time-multiplexed mode.) Moreover, a number of constant inputs must be provided besides the argument, and the network will yield a number of garbage outputs besides the result. Figure 9. An ordinary sequential network computing the sum (mod 2) of a stream of binary digits. Recall that a (+) b = ab +ab....
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