Lecture Notes 2.C

# The function c x y g is chosen so that for a

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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 "bit-conserving," (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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