World Wide Web Computer Literacy Items
5/15/1999 Version
This section involves simple exposition of
number-counting concepts for computer background.
Number Words' Names
Dozen, hour, minute, week involve quantity. Those
words name amounts of
eggs, minutes, seconds or days. (This leads into number bases and modulo
arithmetic.) Continue at Words and Concepts.
Puzzles
Puzzles describe ideas behind computing's use of
binary (odd/even) and other number representation methods (octal, hexadecimal).
What is 11 cut in half (see Roman or Binary)?
Will 9 apples fit in 4 baskets with an odd number in each? This is stated
by a visual diagram Apples-Baskets.
Can a pencil that doesn't leave the paper connect 9 dots
arranged in a square with 3 rows and 3 columns with only 4 straight
lines? Nine Dots diagram.
Can 3 straight line cuts divide a circular pizza into 8 equal
parts? This answers the question by showing the process Pizza Cuts.
Number Bases and a Sequence
Discussion at a more complicated level follows.
Numbers lead to power. They are an example of a general concept.
Number-derived concepts like odd, even help in solving problems.
The odd, even distinction is the same as between on, off.
On and off are at the basis of digital computers' mode of working.
Odd, even (combined with other ideas) is conveyed by puzzles like Apples-baskets.
The cube of any integer can be represented as a sum of adjacent odd
numbers.
Ideas here, namely odd, even, and visualizing cubes readily
lead to a sum of adjacent odd numbers totalling 125.
What's next in this sequence?
10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, __?
Merwyn Sommer contributed this problem that relates to computers.
Building on the preceding we can create an educational unit, as in
the prototype below.
Bases for Counting
Dozen works for eggs; sixty for minutes. Both are number
bases. Common use of ten gives decimal numbers. But for
digital computers that isn't the best choice.
Computers count with zeroes and ones, only two symbols. This causes two, eight and sixteen, even numbers found from repeated
multiplying of two, to play special roles in the digital computer world.
Computers replace counting and symbols based on ten with systems that use
two, eight or sixteen. The names for those systems
are: number base two, binary; eight, octal; and sixteen,
hexadecimal. An example of counting in these bases follows.
Binary three, 11, is octal nine and hexadecimal seventeen.
A table showing comparisons between different number bases or radix
values, tally marks, and lists of valid symbols in base two through
sixteen is Number Systems.
More can be said about number systems used by cultures in different parts of the world, and historic change. Instead this ends here with counting the main theme.