42

Today is 42! Yesterday was 38!

Today is one of 36 dates in the last 11 years that can be confused with a binary number and converted into decimal. Today is 42 in both American and European style dates.

That is, the date, as we usually express it in the US, can be read as if it were a binary number, rather than a date. This is not a conversion, we have to mis-read it as binary.

Most dates cannot be read in binary because they contain digits other than 0 and 1. My birthday,  11/18/63 could not be. It's got all those 8s & 3s and 6s which have no meaning in binary. Binary, base 2, has only two digits available, 0 and 1.  Another system, decimal, base 10, which we are more familiar with which has 10 digits available, zero through nine. (Actually the "di" in digit refers to base 10 (decimal) so that is not an accurate term to use with binary, but it helps to explain it. The correct word for binary digits, is BITS.)

First lets take apart a decimal number for an example: 7703. We know instinctively how big that number is: about eight thousand, or more specifically, it is almost eight times ten times ten times ten. In decimal, when we run out of digits, we increment the next column. When we have counted to 10 by ones, we increment the 10s column to indicate one ten, and we start over at zero with the ones. When we run out of 10s we increment the 100s and then the 1000s. So when we read it, or rather when we do math with it, we are actually reading this:
3 ones
0 tens
7 hundreds (10 to the 2nd, or 10 x 10)
7 thousands (10 to the 3rd, or 10 x 10 x 10)

We add that all up to get the total value represented by that number.

Now let's take today's date apart. In the US we express the date as month-day-year, which for today, Sunday October 10, 2010, we get 10/10/10. If we drop the dividers, that's 101010. It's not actually a binary number, but it looks like one. It's not a decimal number either, it's a combination of bases, but if we were to take it and read it in decimal it would translate like this:

0 one (10 to the 0th, or 1 x 1)
1 ten (10 to the 1st, or 10 x 1)
0 hundreds (10 to the 2nd, or 10 x 10)
1 thousand (10 to the 3rd, or 10 x 10 x 10)
0 ten thousand (10 to the 4th, or 10 x 10 x 10 x 10)
1 hundred thousands (10 to the 5th, or 10 x 10 x 10 x 10 x 10)

0+10+0+1000+0+100,000 = one hundred one thousand and ten.

We do that instinctively with decimal.  We can do the same thing in binary, but we don't have ten digits to play with, only two!  So 101010 is

0 one (2 to the 0th, or 1 x 1)
1 two (2 to the 1st, or 2 x 1)
0 fours (2 to the 2nd, or 2 x 2
1 eight (2 to the 3rd, or 2 x 2 x 2)
0 sixteen (2 to the 4th, or 2 x 2 x 2 x 2)
1 thirty-twos (2 to the 5th, or 2 x 2 x 2 x 2 x 2)

0+2+0+8+0+32 = 10+32 = 42

The powers of two have become more familiar to us recently because computers use them, so the sequence of values: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024..... up to 65536 are numbers that appear frequently in computer related topics.

If we render the date in the European style dd mm yy rather than mm dd yy we would get the same thing today, but something different most days.

The first date that works this was was Jan 1, 2000, it converts to 20 (5 in Europe). The last date that will work is Nov 11, 2011 which converts to 63 in both Europe and the USA.

It is of course arbitrary to choose one base or another. It's just fun because it LOOKS like a binary number, which that doesn't happen often and it converts into a fairly small (two digit) decimal number. We had a few days in January, October & November 2000, 2001 and 2010 that worked, and a few more in 2011, then no more for 89 years.

We could, of course read today's date 101010 in an infinite number of other bases.

In trinary (base 3), 101010 is 0+3+0+27+0+243 = 273 decimal.
or in octal (base 8) it's 33,288 decimal
or duodecimal (base 12) it's 250,572 decimal
or hexadecimal (base 16) it's1,052,688  decimal
or in base 72 it's 1,935,290,952 decimal
and in base 296 it's 2,272,288,717,608 decimal!


Here's the list of all the dates and the result when we mis-read it as binary.

date US style	binary		date Euro style	binary
01/01/2000	20		01.01.2000	5
01/10/2000	24		10.01.2000	6
01/11/2000	28		11.01.2000	7
10/01/2000	36		01.10.2000	9
10/10/2000	40		10.10.2000	10
10/11/2000	44		11.10.2000	11
11/01/2000	52		01.11.2000	13
11/10/2000	56		10.11.2000	14
11/11/2000	60		11.11.2000	15
01/01/2001	21		01.01.2001	21
01/10/2001	25		10.01.2001	22
01/11/2001	29		11.01.2001	23
10/01/2001	37		01.10.2001	25
10/10/2001	41		10.10.2001	26
10/11/2001	45		11.10.2001	27
11/01/2001	53		01.11.2001	29
11/10/2001	57		10.11.2001	30
11/11/2001	61		11.11.2001	31
01/01/2010	22		01.01.2010	37
01/10/2010	26		10.01.2010	38
01/11/2010	30		11.01.2010	39
10/01/2010	38		01.10.2010	41
10/10/2010	42		10.10.2010	42
10/11/2010	46		11.10.2010	43
11/01/2010	54		01.11.2010	45
11/10/2010	58		10.11.2010	46
11/11/2010	62		11.11.2010	47
01/01/2011	23		01.01.2011	53
01/10/2011	27		10.01.2011	54
01/11/2011	31		11.01.2011	55
10/01/2011	39		01.10.2011	57
10/10/2011	43		10.10.2011	58
10/11/2011	47		11.10.2011	59
11/01/2011	55		01.11.2011	61
11/10/2011	59		10.11.2011	62
11/11/2011	63		11.11.2011	63