Tag Archives: binary

Hypercube offsets

Posted on January 30, 2020 by Brent

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 →

Posted in pattern | Tagged binary, bits, cube, diagram, Hasse, hypercube, lattice, subsets | 2 Comments

Post without words #31

Posted on January 23, 2020 by Brent

Posted in posts without words | Tagged binary, bits, cube, diagram, Hasse, hypercube, lattice, subsets | 2 Comments

A few words about PWW #30

Posted on January 22, 2020 by Brent

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

Post without words #30

Posted on January 20, 2020 by Brent

Posted in posts without words | Tagged binary, bits, cube, diagram, Hasse, hypercube, lattice, subsets | 5 Comments

A new counting system

Posted on December 30, 2019 by Brent

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

Posted in arithmetic, counting | Tagged binary, counting, English, humor | 1 Comment

Goldilogs and the n bears

Posted on February 20, 2019 by Brent

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 →

Posted in computation, humor | Tagged bears, binary, goldilocks, search, story | 1 Comment

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

Posted on November 9, 2018 by Brent

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 | Comments Off

Efficiency of repeated squaring: another proof

Posted on September 6, 2018 by Brent

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

Posted on September 1, 2018 by Brent

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

Posted on August 24, 2018 by Brent

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