Digital WiresAlfred 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

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

Digital Wires: hardware implementation as a transistor network

Vin Vout

Cell 1 Cell 2 Cell n

(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.

(a) (b)

Digital Wires:

Hardware implementation as a Boolean network

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 (Boolean network, xor rule)

Digital Wire

Direction ofpulse propagation

Data Program

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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 trafficData 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)

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:

Digital Wire

Wire 1 Wire 2

Given is the state 000111010. What is the pulse one time step later for rule 0? 000000000

Summary: Digital WiresAnalog 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