Articles from 2014 - Exploring Binary

Gangnam Style Video Overflows YouTube Counter

By Rick Regan December 3rd, 2014

On Monday, Psy’s Gangnam Style video exceeded the limit of YouTube’s view counter; this is what Google had to say (hat tip: Digg):

“We never thought a video would be watched in numbers greater than a 32-bit integer (=2,147,483,647 views)…”

2,147,483,647 is 2³¹ – 1, the maximum positive value a 32-bit signed integer can contain.

Google has since fixed the counter, but they didn’t say how (32-bit unsigned integer? 64-bit integer?). (Update: By deduction from this Wall Street Journal article, Google is now using 64-bit signed integers — although the number they cite is 2⁶³, not 2⁶³ – 1.)

The interesing thing is the “Easter egg” Google placed. If you hover your mouse over the counter, it spins like a slot machine; if you hold the mouse there long enough it will show a negative number. But the negative number is not what I expected. Is there a bug in the Easter egg?

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My Fretlight Guitar As a Binary Clock

By Rick Regan November 16th, 2014

With a little research and some USB tracing, I wrote a Windows program — and an Android app — that turns my Fretlight guitar into a BCD mode binary clock!

https://www.exploringbinary.com/wp-content/uploads/FretlightClock.gif — My Fretlight BCD Clock (**click image for video**)

(Update: I now also have a Raspberry Pi version.)

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Decimal/Binary Conversion of Integers in App Inventor

By Rick Regan September 17th, 2014

To complete my exploration of numbers in App Inventor, I’ve written an app that converts integers between decimal and binary. It uses the standard algorithms, which I’ve just translated into blocks.

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App Inventor Computes With Big Integers

By Rick Regan September 17th, 2014

I recently wrote that App Inventor represents its numbers in floating-point. I’ve since discovered something curious about integers. When typed into math blocks, they are represented in floating-point; but when generated through calculations, they are represented as arbitrary-precision integers — big integers.

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Floating-Point Will Still Be Broken In the Year 2091

By Rick Regan September 15th, 2014

Variants of the question “Is floating point math broken?” are asked every day on Stackoverflow.com. I don’t think the questions will ever stop, not even by the year 2091 (that’s the year that popped into my head after just reading the gazillionth such question).

https://www.exploringbinary.com/wp-content/uploads/SO.2091.small.png — A representative floating-point question asked on stackoverflow.com in 2009, projected to be just as popular in 2091 (**click thumbnail to enlarge**)

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Testing Some Edge Case Conversions In App Inventor

By Rick Regan September 12th, 2014

After discovering that App Inventor represents numbers in floating-point, I wanted to see how it handled some edge case decimal/floating-point conversions. In one group of tests, I gave it numbers that were converted to floating-point incorrectly in other programming languages (I include the famous PHP and Java numbers). In another group of tests, I gave it numbers that, when converted to floating-point and back, demonstrate the rounding algorithm used when printing halfway cases. It turns out that App Inventor converts all examples correctly, and prints numbers using the round-half-to-even rule.

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Numbers In App Inventor Are Stored As Floating-Point

By Rick Regan September 11th, 2014

I am exploring App Inventor, an Android application development environment for novice programmers. I am teaching it to my kids, as an introductory step towards “real” app development. While playing with it I wondered: are its numbers implemented in decimal? No, they aren’t. They are implemented in double-precision binary floating-point. I put together a few simple block programs to demonstrate this, and to expose the usual floating-point “gotchas”.

App Inventor Blocks To Display 0.1 to 17 Digits

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GCC Avoids Double Rounding Errors With Round-To-Odd

By Rick Regan January 15th, 2014

GCC was recently fixed so that its decimal to floating-point conversions are done correctly; it now calls the MPFR function mpfr_strtofr() instead of using its own algorithm. However, GCC still does its conversion in two steps: first it converts to an intermediate precision (160 or 192 bits), and then it rounds that result to a target precision (53 bits for double-precision floating-point). That is double rounding — how does it avoid double rounding errors? It uses round-to-odd rounding on the intermediate result.

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