## 1 Introduction: On Noise-Based Logic
### Random Telegraph Waves as a Reference System  
Theoretically speaking, reference signals can be arbitrary types of stochastic processes, provided they are statistically independent and have zero mean.  
For practical purposes, simple two-state binary noises--called random telegraph waves (RTW)--have been proposed as reference signals, including standard ones with \(\pm 1\) values; RTWs with different amplitudes, such as, \(\pm 1\) for the high (1) bit values and \(\pm 0.5\) for the low (0) bit values (see Figures 3-6) to avoid dominant zeros in the amplitude of the Universe; or with complex values [10]; and time-shifted [9] versions that can additionally combine all the above ones. When the reference signals are independent RTWs, the products strings will also be RTWs with zero cross-correlation between different strings (see Figure 5). These schemes have the advantage that binary multiplications and additions can be done accurately and economically by a digital computer while the bandwidth will remain the same order. Moreover, even though the amplitude values in a superposition can fluctuate over an exponentially large range, due to the binary handling of data, this exponential feature requires only a polynomial number of bits of resolution.  
For example, in an RTW-based, \(M\) noise-bit INBL system with amplitudes \(\pm 1\) for the high (1) bit values and \(\pm 0.5\) for the how (0) bit values, the \(R_{10}(t)R_{20}(t)\ldots R_{M0}(t)\) string (corresponding to the \(|00\)... \(0\)\(>\) quantum state vector) has amplitude \(2^{-M}\) and the amplitude of the Universe is bounded by \(\pm 2^{M}\) (see Figures 3-6). For the schemes in the present paper, without giving up generality, we visualize this RTW system. A digital computer with \(2M\)-bit resolution, which easily can be satisfied with proper software, can accurately handle this system. \(M\) in the range of thousands implies some slowdown; however, that slowdown is only polynomial in \(M\).  
Figure 4: Computer simulation [14] of a random telegraph wave carrying the low-bit value of a noise-bit in the asymmetric INBL scheme.  
Figure 5: Computer simulation [14] of the product-string of the number 2 (binary number 000000000000000000000000000000010) in an \(M=32\) noise-bit INBL scheme.  
Figure 3: Computer simulation [14] of a random telegraph wave carrying the high-bit value of a noise-bit in the asymmetric instantaneous-noise-based logic (INBL) scheme.  
In conclusion, an INBL processor is envisioned as a classical PC computer with proper software to handle 2\(M\)-bit resolution and the four basic arithmetic calculations, and a physical true random number generator (TRNG).  
Note: For a classical physical TRNG, the thermal noise of resistors offers the best choice due to the quantum randomness of the phonon scattering of electrons and holes and the extraordinarily large degrees of freedom of these scattered charge carriers resulting in a classical physical enhancement of quantum randomness. Known quantum random generators lack the second feature and they are prone to bias due to various fluctuations in their control degree of freedoms, such as polarizer/beamsplitter angle vibrations, polarization noise of lasers, 1/f noise, etc. Thus, classical physics offers advantageous potential for TRNG, yet their design still requires special attention and possibly hashing.