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Lecture Notes 2.C

# Reversible computing 55 figure ii11 alternative

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Unformatted text preview: vents, represented by conservative-logic gates. conservative computing is essentially conditional rerouting ¶3. Rearranging vs. rewriting: Conventional models of computation are based on rewriting (e.g., TMs, lambda calculus, register machines, term rewriting systems, signals, C. REVERSIBLE COMPUTING 55 Figure II.11: Alternative notation for Fredkin gate. Post and Markov productions). But we have seen that overwriting dissipates energy (and is non-conservative). ¶4. In conservative logic we rearrange bits without creating or destroying them. (No inﬁnite “bit supply” and no “bit bucket.”) ¶5. Fredkin gate: The Fredkin gate is a conditional swap operation (also called CSWAP): (1, a, b) 7! (1, a, b), (0, a, b) 7! (0, b, a). The ﬁrst input is a control signal and the other two are data signals. Here, 0 signals a swap, but some authors use 1 to signal a swap. See Fig. II.10 and Fig. II.13. Fig. II.11 shows an alternative notation for the Fredkin gate. ¶6. Note that it is reversible and conservative. ¶7. Universal: The Fredkin gate is a universal Boolean primitive for conservative logic. C.5 Conservative logic circuits ¶1. “A conservative-logic circuit is a directed graph whose nodes are conservativelogic gates and whose arcs are wires of any length [Fig. II.12].” 56 CHAPTER II. PHYSICS OF COMPUTATION A conservative-logic circuit is a directed graph whose nodes are conservative-logic gates and whose arcs are wires of any length (cf. Figure 3). 3. COMPUTATION IN CONSERVATIVE-LOGIC CIRCUITS; CONSTANTS AND GARBAGE In Figure 4a we have expressed the output variables of the Fredkin gate as explicit functions of the input variables. The overall functional relation-ship between input and output is, as we have seen, invertible. On Figure that closed and (b) open computing are often noninvertible. Thus, special the other hand, the functions3. (a)one is interested in conservative-logic circuits. provisionsFigure II.12: in the closed the Fredkin gate conservative-logic of any invertible function that is...
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