Unformatted text preview: Exponential growth of garbage: This is a signiﬁcant problem if
dissipative circuits are naively translated to conservative circuits because:
(1) the amount of garbage tends to increase with the number of gates,
and
(2) with the naive translation, the number of gates tends to increase
exponentially with the number of input lines.
“This is so because almost all boolean functions are ‘random’, i.e., cannot be realized by a circuit simpler than one containing an exhaustive
lookup table.”
¶3. However there is a way to make the garbage the same size as the input
(in fact, identical to it).
¶4. First observe that a combinational conservativelogic network (one with
no feedback loops) can be composed with its inverse to consume all
garbage (Fig. II.17).
¶5. The desired output can be extracted by a “spy circuit” (Fig. II.18). Figure 20. (a) Computation of y = f(x) by means of a combinational conservativelogic network . (b) This
computation is "undone" by the inverse network, 1 Figure 20. (a) Computation of y = f(x) by means of a combinational conservativelogic network . (b) This
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CHAPTER the PHYSICS OF 1
computation is "undone" byII. inverse network, COMPUTATION
Figure 21. The network obtained by combining and 1 'looks from the outside like a bundle of parallel
wires. The value y(=f(x)) is buried in the middle.
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
1
Figure 21.igure networkComposition of combinational conservativelogic like a bundle of parallel
F The II.17: obtained by combining and 'looks from the outside Figure 23, and
are sent through a "black...
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 Fall '13
 BruceMacLennan
 Logic gate, fredkin gate, Fredkin

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