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Unformatted text preview: "garbageless" circuit for computing the function y = f(x). Inputs C1,..., Ch and X1,…., Xm are
returned unchanged, while the constants 0,...,0 and 1,..., 1 in the lower part of the circuits are replaced by the
C. REVERSIBLEresult, y1,...., yn and its complement, ¬y1,...., ¬yn
COMPUTING
61 Figure 24. The conservativelogic scheme for garbageless computation. Three data registers are "shot"
Figure II.20: “The conservativelogic scheme for garbageless computation.
through a conservativelogic blackbox F. The register with the argument, x, is returned unchanged; the
cleanThree data registers are ‘shot’ through aappropriate supply of input constants,The as a
register on top of the figure, representing an conservativelogic blackbox F . is used
register the computation (cf. the c and g lines in Figure 23) but is clean clean at on
scratchpad during with the argument, x, is returned unchanged; thereturnedregister the end of the
top of the the tokens on the register the bottom of the figure input constants, is
computation. Finally, ﬁgure, representing anatappropriate supply of are rearranged so as to encode the
result y and its complement ¬y
used as a scratchpad during the computation (cf. the c and g lines in Figure [II.19]) but is returned clean at the end of the computation. Finally, the (a)
The "argument" register, containing a given arrangement of tokens x, is returned unchanged. The
tokens on the register at the bottom of the ﬁgure are rearranged so as to
capacity of this register is m, i.e., the number of bits in x. encode the result y and its complement ¬y ” (Fredkin & To↵oli, 1982) (b)
A clean "scratchpad register" with a capacity of h tokens is supplied, and will be returned clean.
(This is the main supply of constantsnamely, c1, . . . , ch in Figure 23.) Note that a clean register means one
with all 0's (i.e., no tokens), while we used both 0's and l's as constants, as needed, in the construction of
Figure 10. ¶6....
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 Fall '13
 BruceMacLennan

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