Lecture Notes 2.C

# A token at a given position on the board represents a

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Unformatted text preview: box" F, which represents the conservative-logic circuit of network withwhen they its inverse tokenswires. The value y(=f(x)) is buried in the middle. ↵ added. Let reappear some of the to consume have garbage. [ﬁg. from Fredkin away oroli (1982)] us follow this may the been moved, but none taken & To process, register by register. The remarkable achievements of this construction are discussed below with the help of the schematic representation of Figure 24. In this figure, it will be convenient to visualize the input registers as "magnetic bulletin boards," in which identical, undestroyable magnetic tokens can be moved on the board surface. A token at a given position on the board represents a 1, while the absence of a token at that position represents a 0. The capacity of a board is the maximum number of tokens that can be placed on it. Three such registers are sent through a "black box" F, which represents the conservative-logic circuit of Figure 23, and when they reappear some of the tokens may have been moved, but none taken away or added. Let us follow this process, register by register. Figure 22. Figure II.18: The by an arbitrary line (a) can be inspected in a nondestructive way in the "spy" The value a carried “spy circuit” for tapping into the output. Note that by device in (b). the diagram the 0 and 1 constant inputs are switched (or, equivalently, the a and a outputs are switched). See also the FAN-OUT circuit in Fig. II.15. [ﬁg. from Fredkin & To↵oli (1982)] Figure 22. The value a carried by an arbitrary line (a) can be inspected in a nondestructive way by the "spy" device in (b). Figure 23. A "garbageless" circuit for computing the function y = f(x). Inputs C1,..., Ch and X1,…., Xm are Figure II.19: Garbageless circuit. (Fredkin & To↵oli, 1982) returned unchanged, while the constants 0,...,0 and 1,..., 1 in the lower part of the circuits are replaced by the result, y1,...., yn and its complement, ¬y1,...., ¬yn Figure 23. A...
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## This document was uploaded on 03/14/2014 for the course COSC 494/594 at University of Tennessee.

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