Lecture Notes 2.C

Is used register the computation cf the c and g lines

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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 conservative-logic scheme for garbageless computation. Three data registers are "shot" Figure II.20: “The conservative-logic scheme for garbageless computation. through a conservative-logic black-box 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 conservative-logic black-box 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 constants-namely, 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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