### 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.