Articles in the ‘Binary numbers’ Category

Nines in Binary

(Published June 10th, 2009)

I discovered a cool property of positive integers of the form 10ⁿ-1, that is, integers made up of n digits of 9s: they have binary representations that have exactly n digits of trailing 1s. For example, 9,999,999 in decimal is 100110001001011001111111 in binary.

The property is interesting in and of itself, but what is more interesting is the process I went through to discover it. It’s a small-scale example of experimental mathematics: I observed something interesting, experimented to collect more data, developed a hypothesis, and constructed a proof.

Doing Decimal/Binary Conversions with Wolfram Alpha

By Rick Regan

(Published May 29th, 2009)

Wolfram Alpha can do many types of calculations, including conversions between numbers in different bases. I’ll demonstrate by showing examples of decimal to binary and binary to decimal conversion.

How I Taught My Mother Binary Numbers

By Rick Regan

(Published May 26th, 2009)

I introduced my mother to binary numbers a few weeks ago when I showed her my One Hundred Cheerios in Binary poster. It shows the decimal number 100 in binary — 1100100. She’s not an engineer but she’s good with numbers, so I knew she would get it — if only I could find the right way to explain it. Two days ago, I found the right way.

Google is a Binary, Hex, and Octal Number Calculator

By Rick Regan

(Published February 25th, 2009)

Did you know you can use Google as a calculator? Type 1 + 2 + 4 + 8 + 16 + 32 into Google’s search box and you’ll get 63 as the result.

Did you know you can use the calculator with numbers in different bases? It can convert numbers between decimal, binary, hexadecimal, and octal, as well as do arithmetic in those bases. To work in a non-decimal base, just prefix numbers as follows: 0b for binary, for example, 0b1010; 0x for hexadecimal, for example, 0xFF; and 0o for octal, for example, 0o701.

What a Binary Counter Looks and Sounds Like

By Rick Regan

(Published February 22nd, 2009)

This is what it sounds like to count from 1 to 255 in binary (music courtesy of Jake Joaquin). It’s so simple, reflecting the simplicity of binary code; yet it speaks volumes about the structure of binary numbers. It inspired me to draw a picture, so I could see what binary counting looks like as well:

Visual Interpretation of the Binary Clicker (click image for higher resolution).

A Pattern in Powers of Ten and Their Binary Equivalents

By Rick Regan

(Published February 6th, 2009)

In my article “One Hundred Cheerios in Binary”, I made a comment about the decimal number 100, and its binary equivalent, 1100100:

“And will they wonder if the two sub strings of ‘100’ in the binary number have any significance?”

What I meant is if a novice might wonder if a decimal string made up of 1s and 0s must appear in its binary equivalent. Of course that’s not true in general, but it is true for nonnegative powers of ten — the trailing digits of the binary number will match the power of ten!

One Hundred Cheerios in Binary

By Rick Regan

(Published February 2nd, 2009)

My son had to do a project for his 100th day of first grade. Since I’ve been teaching him binary — he knows the powers of two from 1 to 512 — we decided to incorporate it into his project. His assignment was to assemble 100 objects in a creative way. This is as creative as I get:

One Hundred Cheerios®, in Binary.

A Twelve Cent Binary Calendar

By Rick Regan

(Published January 1st, 2009)

Do you have twelve coins handy? You can lay them out on a piece of cardboard to keep track of the month, day, and day of the week, as shown here at Evil Mad Scientist Laboratories. Here’s the one I made:

Thursday, January 1st, in pennies.

How to Read a Binary Clock

By Rick Regan

(Published November 23rd, 2008)

What is a binary clock? Before doing a web search I would have guessed this:

My Fake Binary Alarm Clock (time is 6:43 PM).

6:43 PM on my fake binary alarm clock (courtesy photo-editing software).

In other words, a regular digital clock, except with binary numerals instead of decimal numerals. But as far as I know, a clock like this doesn’t exist. If you search for “binary clock,” you get a clock of a different design, one like this: