Centennial Birthday of Claude E. Shannon the Math and EE Pioneer

Dr. Claude E. Shannon was born 100 years ago tomorrow. He contributed greatly to the fields of engineering, communications, and computer science but is not a well known figure, even to those in the field. However, his work touches us all many times each day. The network which delivered this article to your computer or smartphone was designed upon important theories developed by Dr. Shannon.

Shannon was born and raised in Michigan. He graduated from the University of Michigan with degrees in Mathematics and Electrical Engineering. He continued his graduate studies at Massachusetts Institute of Technology (MIT) where he obtained his MS and PhD. He worked for Bell Laboratories on fire-control systems and cryptography during World War II and in 1956 he returned to MIT as a professor.

shannon-0Shannon’s first impactful contribution was his masters thesis which took the Boolean Algebra work of George Boole and applied it to switching circuits (then made up of relays). Before his work there was no formal basis for the analysis of switching systems, like telephone networks or elevator control systems. Shannon’s thesis developed the use of symbolic notation to represent networks and applied simplifying rules to optimize the system. These same rules later translated to vacuum tube and transistor logic aiding in the development of today’s computer systems. The thesis — A Symbolic Analysis of Relay and Switching Circuits — was completed in 1937 and subsequently published in 1938 in the Transactions of the American Institute of Electrical Engineers.

Shannon’s doctoral work continued in the same vein of applying mathematics someplace new, this time to genetics. Vannevar Bush, his advisor, commented, “It occurred to me that, just as a special algebra had worked well in his hands on the theory of relays, another special algebra might conceivably handle some of the aspects of Mendelian heredity”. Shannon’s work again is revolutionary, providing a mathematical basis for population genetics. Unfortunately, it was a step further than geneticists of time could take. His work languished, although interest increased over time.

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From Gates to FPGA’s – Part 1: Basic Logic

It’s time to do a series on logic including things such as programmable logic, state machines, and the lesser known demons such as switching hazards. It is best to start at the beginning — but even experts will enjoy this refresher and might even learn a trick or two. I’ll start with logic symbols, alternate symbols, small Boolean truth tables and some oddball things that we can do with basic logic. The narrative version is found in the video, with a full reference laid out in the rest of this post.

Invert

1The most simple piece of logic is inversion; making a high change to low or a low change to high. Shown are a couple of ways to write an inversion including the ubiquitous “bubble” that we can apply almost anywhere to imply an inversion or a “True Low”. If it was a one it is now a zero, where it was a low it is now a high, and where it was true it is now untrue.

AND

2Moving on to the AND gate we see a simple truth table, also known as a Boolean Table, where it describes the function of “A AND B”. This is also our first opportunity to see the application of an alternate symbol. In this case a “low OR a low yields a low”

NAND

3Most if not all of the standard logic blocks come in an inverted form also such as the NAND gate shown here. The ability to invert logic functions is so useful in real life that I probably used at least three times the number of NAND gates as regular AND gates when doing medium or larger system design. The useful inversion can occur as spares or in line with the logic.

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7400 series logic simulator

logic

Atanua is a real time logic simulator to help people learn some of the basics of electronics. Focusing mainly on logic, as opposed to power, this is a fantastic tool to learn with. They have done a fantastic job of making it easy to use as well as good looking. We can see this as being a must have piece of software for any hacker. There is a free version available as long as you aren’t using it commercially.

[Thanks ellisgl]