Digital Wires Alfred Hubler, a-hubler@illinois, Physics, UIUC server10.how-why/blog

1. Digital Wires • Alfred Hubler, a-hubler@illinois.edu, Physics, UIUC http://server10.how-why.com/blog • Analog wires are used to move energy (power lines, power grid) and information (data transmission lines, Internet) in electrical networks. • However, most dynamical systems with more than 7 degrees of freedom are chaotic => the dynamics of large networks of analog wires is unstable => congestions & cascading failures • Digital wires: Wires that propagate only patterns of rectangular pulses • Specific advantages of digital wires: • - Fixed pulse shape (increased reliability & speed); • Robust against electric smog (increased reliability & speed); • - No cross talk (increased reliability & speed); • - No echoes (increased reliability & speed); • Adjustable pulse speed (increased adjustability); • Encryption (increased security); • Digital wire can be general purpose computers (increased adjustability). • Neurons are digital wires. Digital wires move information in parallel. Digital Wire

2. Graphical depiction of a “Digital Wire” formed by imposing circular boundary conditions on a CA. A digital wire implemented by a CA has notable advantages over copper wires, such as isolating defects. By choosing the appropriate rule, the effects of a defect such as a short circuit can be isolated to a single cell site, rather than propagating the defect along the entire wire, as copper wires do. Digital wires

3. Digital Wires: hardware implementation as a transistor network Vin Vout Cell 1 Cell 2 Cell n (a) (b) (a) A digital wire constructed of resistors and pnp transistors. (b) Experimental measurement of the input-output response of the pnp-transisator digital wire. The sharp transition at 77% of the total supply voltage results in a noise immunity threshold. In order for noise to affect the outcome of a signal, it must exceed this threshold.

4. Digital Wires: Hardware implementation as a Boolean network

5. Digital wires: a simple model Definition: A digitial wire is a long network of cells. Digital pulses travel along the digital wire, according to the following rule: Ax+1,y = f (Ax,y-1, Ax,y, Ax,y-1) -i.e. the state of the cell Ax+1,y =0,1, depends only on the “upstream” neighbors. Discussion: Digital wires can be viewed as hardware implementations of elementary cellular automata (S. Wolfram). Therefore a digital wire can be a general purpose computer. Digital Wire Digital wire (Boolean network, xor rule)

6. Digital Wire Data Program Direction of pulse propagation

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11. Digital Wire • Discussion, continued … • Digital wires on various scales: • -nano- level: thin film transistor networks (parallel , reliable input for CPUs, may replace CPU), quantum dot networks, neurons (brain) • Atomic level: electron hopping from atom to atom along a path on a macro molecule (hard ware implementations of neural nets) • Microscopic level: transistor networks • Mesoscopic level: Boolean networks, Field programmable gate arrays (image processing) • Macroscopic level: power lines with phase sensitive switches every 10 miles (no cascading power failures), city traffic • Data transmission lines versus power lines: • There is energy traveling with every pulse. Computation does not necessarily consume much power (conservative computation). • Periodic pulses can produce a lot of power. • Pulses that carry information look random. • H. Higuraskh, A. Toriumi, F. Yamaguchi, K. Kawamura, A. Hübler, Correlation Tunnel Device, U. S. Patent # 5,679,961 (1997)

12. Digital Wire • Discussion, continued … • Different cellular automata rules: • -Rule 110: general purpose computer • Rule 204: identity rule • Rule 30: random number generator • Rule 254: self-repairing pulses • Rule 0: trivial • Merging data from different digital wires: Given is the state 000111010. What is the pulse one time step later for rule 0? 000000000 Wire 1 Wire 2

13. Summary: Digital Wires • Analog wires are used to move energy (power lines, • power grid) and information (data transmission lines, • Internet) in electrical networks. • -Dynamical systems with more than 7 degrees of freedom are chaotic (Lee Rubel )=> the dynamics of large networks of analog wires are unstable. • Digital wires: wires that propagate only patterns of rectangular pulses • Specific advantages of digital wires: • - Fixed pulse shape (increased reliability) • Robust against electric smog (increased reliability) • - No cross talk (increased reliability) • - No echoes (increased reliability) • Adjustable pulse speed (increased adjustability) • Encryption (increased security) • Digital wire can be general purpose computer s(increased adjustability) • Neurons are digital wires. • Alfred Hubler, a-hubler@illinois.edu, Physics, UIUC http://server10.how-why.com/blog Digital Wire