It's All About The Year, The New Year ... 2015

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(C)Copyright 2015, C. Burke.

And you know that he probably does, too.

HAPPY NEW YEAR!

The new year, 2015, brings some interesting numbers when converted into other bases. Granted, I find most numbers interesting in some way, but these still have interesting features.

In base 2 (binary), we have a palindrome; it's the same backward. The 0 in the middle means that we are 32 years away from all 1s and 33 away from rolling over the counter and adding another digit.

In base 3 (trinary), the number can be broken down into 2 20 21 22, which is somewhat sequential.

In base 4 (tetranary(?), ah skip it!), which is related to base 2 by virtue of being a power of 2, we get 133 133. It's not the palindrome that base 2 is; it's something more fun!

I don't have much to say about bases 5, 6, or 7. They have pairs of numbers, but that's hardly surprising. Two of them look like zip codes, so I checked: 31030 is Fort Valley, Georgia and 13155 in an area of upstate New York, south of Syracuse. (I thought it might be a section of Queens, in New York City, which is why I checked. Nope.) Last year, base 5 was 31024, which had all five available numbers in it, but we're a year too late for that.

In base 8 (octal), another power of 2, we get another repetition: 3737. Wonderful.

In base 9, meh. I hope everyone could figure out what base 10 was, so I skipped it. Base 11 likewise is boring as no alphabetic characters were required to substitute for numbers greater than 9.

In base 12, it gets interesting. While 12 is a multiple of 2, it isn't a power of 2. Using alphabetic characters, it's 11BB, but the "B" is a stand in for 11, so it's actually 1,1,11,11. Practically binary! (But it's not.) Note: in bases larger than 10, such as Sexagesimal, it is common to write the numbers in decimal form (no letters) and separate the powers with commas.

In base 13, we have 11, 12, 0 because the year is divisible by 13. Last year was 11, 11, 12. The year before 11, 11, 11. (You see: there's always something to be found!)

Finishing up, in base 14, 10 and 3 make 13. And we end with snoozy bases 15 and 16 (hexadecimal), which aren't all that interesting this year, although next year is 7E0 or 7, 14, 0. Something to look forward to!

Happy New Years Eve 2015

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(C)Copyright 2014, C. Burke.

At least he came to give moral support. Two to the thirteenth won't be around for a while!

Two notes: First, 2^11 - 2^5 - 1 = 2015. That is to say, if all the powers of two, up to 10, were included, the sum would be 2047, which is one less that 2 to the 11th, which is 2048. Second, let's not forget the Y2048 bug! Or maybe the Y2(11) bug, just to be creative. Yes, it's true -- some really old computers, which will be really, really old 33 years from now, will have a problem handling the year as 2 to the 11th power. It should prove as Earth-shattering as Y2K did.

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UPDATE: The Making of a Webcomic

This comic started with an 11-digit binary number, 10 ones and 1 zero. I thought it would be funnier if I used the powers of 2 instead, so I needed 11 twos. And then I decided to include the next power as an extra gag. So I needed to draw 12 twos.

Rather than use one of the two twos I usually use and instead of typing the twos, I decided to try on of the paint programs on my tablet and doodled them. I was worried that they might be too snakelike -- and then I was worried that I'd doodled a row of ducks. (I have to keep this in mind if I ever need ducks again.) Then I made the smaller numeric exponents from 12 on down to 0. Colored it in and emailed it to me PC.

Putting it together I realized that I had too many exponents and not enough twos! Oops! I made a mistake. BUT I PICKED THE WRONG MISTAKE! The problem wasn't that I didn't have enough 2s (and quickly created an extra). The problem was that if the lowest exponent was zero, then the highest exponent I needed was 11.

And somehow though all the checking and proofreading -- including all that stuff above (which I have since corrected) -- none of this popped into my head. Of course, moving to 2^11 power would be a bigger problem than moving to 2^12. Some things are stored as 10 bits (I don't know why, but they were) but nothing would be stored as 11 bits (well, maybe -- programmers are strange).

Anyway, the correction has been made. HAPPY NEW YEAR!!

BASE Jump

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(C)Copyright 2011, C. Burke. All rights reserved.

Update: 11/16/21: Welcome to all the Daily Maths people who found this page from a link on the calendar puzzle! Thank you for stopping by! I see you!

Remember, kids, don't try this at home! Well, I guess you really can't try this at home unless you live in a really tall building or have a cliff in your backyard . . .

(C)Copyright 2011, C. Burke. All rights reserved. Remember, kids, don't try this at home! Well, I guess you really can't try this at home unless you live in a really tall building or have a cliff in your backyard . . .

Base

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(C)Copyright 2011, C. Burke. All rights reserved.


What can I add here? I don't know. Third base.

Bases

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(C)Copyright 2010, C. Burke. All rights reserved.


It was supposed to just be the Christmas specials, but I couldn't pass up the other ones.
The images were found around the web.