Unformatted text preview: for the quantities in which signals are encoded that conservative logic derives its
name.
It must be noted that reversibility (in the sense of mathematical invertibility) and conservation are
independent properties, that is, there exist computing circuits that are reversible but not "bitconserving,"
(Toffoli, 1980) and vice versa (Kinoshita, 1976).
Figure 5. Realization of f by using source and sink. The function : (c, x) (y, g) is chosen so that, for a
particular value of c, y = f(x).
Terminology: source, sink, constants, garbage. Given any finite function , one obtains a new function f
"embedded" in it by assigning specified values to certain distinguished input lines (collectively called the Figure 4. Behavior of the Fredkin gate (a) with unconstrained inputs, and (b) with x2 constrained to the
C. REVERSIBLE COMPUTING
57
value 0, thus realizing the AND function. Figure 5.FRealization of f by using sourcef bysink.uThe function and x) (y, The chosen so that, for a
igure II.14: “Realization of and
sing source : (c, sink. g) is function
particular value ofac,particular value of c, y = f (x).”
y = f(x).
: (c, x) 7! (y, g ) is chosen so that, for (Fredkin & To↵oli, 1982) Terminology: source, sink, constants, garbage. Given any finite function , one obtains a new function f
"embedded" in it by assigning specified values to certain distinguished input lines (collectively called the
source) and disregarding certain distinguished output lines (collectively called the sink). The remaining
input lines will constitute think of the, gate asremaining output lines,the result.wire as being (Figure
¶2. We can the argument and the instantaneous and the unit This construction
5) is called a realization of f by means ofwe using make aand sink. In (or imagineyintervening the source
a unit delay, of which
can source sequence realizing f b means of ,
lines will be fed with constant values, i.e., with values that do not depend on the argument. On the other
identity gates).
hand, the sink lines in general will yie...
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 Fall '13
 BruceMacLennan
 Logic gate, fredkin gate, Fredkin

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