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6 discrete time dynamical system a conservative logic

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Unformatted text preview: ld values that depend on the argument, and thus cannot be used as input constants for a new computation. Such values will beis a closed (or . isolated) physical life, this ¶3. Closed vs. open: A closed circuit termed garbage (Much as in ordinary system. An open circuit has external inputs and outputs. ¶4. The number of outputs must equal the number of inputs. ¶5. It may be part of a larger conservative circuit, or connected to the environment. ¶6. Discrete-time dynamical system: A conservative-logic circuit is a discrete-time dynamical system. ¶7. Degrees of freedom: The number N of unit wires in the circuit is its number of DoF. The numbers of 0s and 1s at any time is conserved, N = N0 + N1 . C.6 Constants and garbage ¶1. The Fredkin gate can be used to compute non-invertible functions such as AND, if we are willing to provide appropriate constants (called “ancillary values”) and to accept unwanted outputs (see Fig. II.13). garbage is not utterly worthless material. In Section 7, we shall show that thorough "recycling" of garbage is not only possible, but also essential for achieving certain important goals.) By a proper selection of source and sink lines and choice of constants, it is possible to obtain from the Fredkin gate other elementary Boolean functions, such as OR, NOT, and FAN-OUT (Figure 6). In order to synthesize more complex functions one needs circuits containing several occurrences of the Fredkin gate. For example, Figure 7 illustrates a l-line-to-4-line demultiplexer. Because of the delays represented by the wires, this is formally a sequential network. However, since no feedback is present and all paths from the argument to 8 garbage is traverse worthless material. In Section 7, wewires, the analysis "recycling" of garbage is result not utterly the same CHAPTER II.shall show that OF COMPUTATION unit 5 the ot only possible, but also essential number of certain important goals.)thorough of this circuit is substantially PHYSICS nof a combinational network.4 achieving for identic...
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