Posts Tagged ‘Ivor Page’

220px-Full_Adder.svgAddition is the most elementary arithmetic operation required of computers. Their invention and development has almost entirely been to do arithmetic extremely fast.  I will present the simplest binary adder circuits (ripple carry adder), show some surprising results about carry propagation, develop carry look-ahead circuits for log-time addition, and then talk about redundant number systems and constant time addition and, consequently, log-time multiplication.
I will also present residue number systems that enable constant time addition and multiplication.
It’s all integer math, modulo arithmetic, and some simple logic circuits.

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If you were not among the fortunate students who heard Dr. Ivor Page give his December 10 talk on “Thinking as Exercise” here is a video that illustrates one of the many fascinating problems discussed.

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In this talk we will solve problems from multiple areas of mathematics and computer science. We will discuss Euler circuits and paths and their use in designing postman routes, finding Steiner points with soap bubbles, counting cannon balls in stacks, continued fractions, the ubiquity of Fibonacci numbers in Computer Science and nature, problems that are intractable for computers, and more.

Bring your brain!

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