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Unformatted text preview: Fig. II.19 shows the Margolus arrangement 0's can be used in this register without loss of
However, a proof due to N. general shows that all for garbageless computation.
generality. In other words, the essential function of this register is to providenumber output with spare
This requires the provision of n new constants (n = the computation
room rather than tokens.
Finally, we supply a clean "result" register of capacity 2n (where n is the number of bits in y). For
this register,7. Consider that the topschematic diagram in Fig. II.20.
¶ clean means the more half is empty and the bottom half completely filled with tokens. The ¶8. Think of arranging tokens (representing 1-bits) in the input registers,
both to represent the input x, but also a supply of n of them in the
black lower square.
¶9. Run the computation.
¶10. The input argument tokens have been restored to their initial positions.
The 2n-bit string 00 · · · 0011 · · · 11 in the lower register has been rearranged to yield the result and its complement y y .
¶11. Restoring the 0 · · · 01 · · · 1 inputs for another computation dissipates
energy. 62 CHAPTER II. PHYSICS OF COMPUTATION Figure II.21: Overall structure of ballistic computer. (Bennett, 1982) ¶12. Feedback: Finite loops can be unrolled, which shows that they can
be done without dissipation.
(Cf. also that billiard balls can circulate in a frictionless system.) C.9 Ballistic computation “Consider a spherical cow moving in a vacuum. . . ”
¶1. Billiard ball model: To illustrate dissipationless ballistic computation, Fredkin and To↵oli deﬁned a billiard ball model of computation.
¶2. It is based on the same assumptions as the classical kinetic theory of
gasses: perfectly elastic spheres and surfaces.
In this case we can think of pucks on frictionless table.
¶3. Fig. II.21 shows the general structure of the billiard ball model.
¶4. 1s are represented by the presence of a ball at a location, and 0s by
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- Fall '13