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7.6: Reversible Computers and Noise

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    52424
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    Reversible computers, however, remain extremely controversial in engineering circles. The catch is noise. Shannon's theorem, for example, requires \(E_{min} = k_{B}T\ln(2)\) for the transmission of one bit of information in a noisy channel. This applies even in a reversible system such as the billiard ball collision gate. In fact, billiard ball gates are extremely sensitive to errors. Given a slight error in the trajectory or timing of one ball and a billiard ball computer would accrue a large number of errors.

    A billiard ball computer could be made more robust and noise resistant by including trenches to guide the balls. But the trench guides the balls by dissipating that component of the ball's momentum that would otherwise drive it off its designed trajectory. Thus, the trenches inevitably lead to energy dissipation.

    In contrast, let's briefly look at noise in CMOS circuits. The transfer function of a CMOS inverter is shown in Figure \(\PageIndex{1}\). We see that close to the switching voltage, the inverter has very large gain, \(A_{V}\):

    \[ A_{V} = \frac{dV_{out}}{dV_{in}} \gg 1 \label{7.6.1} \]

    The gain protects the inverter against noise. For example, consider two cascaded inverters. Assume some noise is added to the output of the first inverter. The noise margin tells us the minimum amount of noise required to cause an error at the output of the second inverter; see Figure \(\PageIndex{2}\).

    Thus, many device engineers argue that without gain no computation system is practical. And since reversible computers do not dissipate power it is not clear how they can amplify a signal, rendering them always subject to the adverse effects of noise.

    Screenshot 2021-05-27 at 15.18.34.png
    Figure \(\PageIndex{1}\): Transfer characteristics of a CMOS inverter. \(V_{IL}\) and \(V_{IH}\) are defined as the threshold of low and high inputs, respectively. Note that the large gain means that \(V_{OL} < V_{IL}\) and \(V_{OH} > V_{IH}\), helping protect signal integrity against the effects of noise.
    Screenshot 2021-05-27 at 15.19.46.png
    Figure \(\PageIndex{2}\): The noise margin in a digital circuit is the minimum input noise voltage required to cause an error at the output of the next gate. The greater the gain, the greater the noise margin.

    7.6: Reversible Computers and Noise is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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