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# Tag Archives: binary

## Hypercube offsets

In my previous posts, each drawing consisted of two offset copies of the previous drawing. For example, here are the drawings for and : You can see how the drawing contains an exact copy of the drawing, plus another copy … Continue reading

## A few words about PWW #30

A few things about the images in my previous post that you may or may not have noticed: As several commenters figured out, the th diagram (starting with ) is showing every possible subset a set of items. Two subsets … Continue reading

Posted in posts without words
Tagged binary, bits, cube, diagram, Hasse, hypercube, lattice, subsets
4 Comments

## A new counting system

0 = t__ough 1 = t_rough 2 = th_ough 3 = through So, for example, trough through tough though though. English is so strange.

## Goldilogs and the n bears

Once upon a time there was a girl named Goldilogs. As she was walking through the woods one day, she came upon a curious, long house. Walking all round it and seeing no one at home, she tried the door … Continue reading

## The wizard’s rational puzzle (solutions, part 2)

At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading

Posted in arithmetic, challenges, logic, programming, puzzles, solutions
Tagged arithmetic, binary, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, search, wizard

## Efficiency of repeated squaring: another proof

In my previous post I proved that the “binary algorithm” (corresponding to the binary expansion of a number ) is the most efficient way to build using only doubling and incrementing steps. Today I want to explain another nice proof, … Continue reading

Posted in computation, proof
Tagged binary, double, efficiency, exponent, increment, proof, repeated, squaring, steps
3 Comments

## Efficiency of repeated squaring: proof

My last post proposed a claim: The binary algorithm is the most efficient way to build using only doubling and incrementing steps. That is, any other way to build by doubling and incrementing uses an equal or greater number of … Continue reading

Posted in computation, proof
Tagged binary, double, efficiency, exponent, increment, proof, repeated, squaring, steps
2 Comments

## Efficiency of repeated squaring

As you probably realized if you read both, my recent post without words connects directly to my previous post on exponentiation by repeated squaring Each section shows the sequence of operations used by the repeated squaring algorithm to build up … Continue reading

Posted in computation
Tagged binary, double, efficiency, exponent, increment, repeated, squaring, steps
7 Comments