- Your quiz Friday will involve writing numbers in any given
base, and, in particular, Mayan numbers. There may be something about
Morse Code, and trees.
- You might check out these other base videos (I've put the links on
your assignment page):
- Schoolhouse Rock strikes again: Little Twelve Toes
- Tom Lehrer strikes, too: New Math -- a lesson in base-8 arithmetic
- New
"largest prime" discovered! Discoverer may win $3000 prize....
Thanks, Victoria, for catching this in the news. Victoria did win a "get-out-of-quiz-free" card, for going above and beyond the call of duty.
Notice that this is a "Mersenne Prime", the 48th known --
What is it about powers of two?
Others Mersenne Primes:
breaks it!)
-
- Can you make the trick work? You should be able to do it every time!
- How does the trick work? What's the secret?
It turns out that the Fraudini trick will be important when it comes to doing Egyptian math. The ability to write numbers this way is historically very important.
Computers operate in a "binary world", a world of "on" and "off": electronic gates are either open or closed, so computer designers and programmers have used the binary system consisting of only two digits -- 0 and 1 -- since the dawn of computing.
Convert the following base-10 numbers to binary:
- 7
- 12
- 36
- 59
- 1001
- 1101
- 110010
- 101110
(And it's even easier in binary, since you just add up the powers of two that have a 1 in their position -- the Fraudini trick.)
Let's try some hexadecimal conversions. But first, here's why computer scientists have used hex (e.g. for colors on web pages):
Four binary digits together can represent any base-10 number from 0 to 15. To create a more condensed representation of numbers, hexadecimal numbers (base-16), are used instead. So let's convert some binary numbers to hex numbers first:
Convert the following binary numbers to hexadecimal (base-16) numbers:
- 1001
- 1101
- 110010
- 101110
- 10011101110010101110
Numbers that are really long in binary are much shorter in base 16 (about 1/4th as long), and in base-10. Here's a general rule that you can believe in:
(but you'll perhaps have ugly digits, as the Babylonians do, or the Mayans, or even the ugly A,B,C digits of the hex system).
What's the connection to binary?
(This explains why I want you to write the answer primitive count string the way that I do!)
Now you have a great way of checking your primitive counts, or of writing binary numbers: they're exactly the same. It turns out that primitive people may have been counting in binary, and today our best computers, the ones that find great big prime numbers (that are powers of 2 -- minus 1), do their counting the same way.
Two fingers are enough!