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<H3><B>Bases for Counting</B></H3>
**Bases for Counting**

*Dozens* work for eggs as *sixties* do for minutes. General
agreement has been to use *tens* since numbers took the current
form. For digital computers that choice isn't best.

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
and an example of counting in them is next.

*Binary* three, 11, is *octal* nine and
*hexadecimal* seventeen. For detailed information please click Number Forms.

Problem: The square of 24 in base b equals 554 in base b. What is base
b?

Number systems used by different world cultures and historic change is fascinating (see Sumeria; a Cooper Union *Civilization* course led to this subject).
Still the theme of *Computers and Mathematics* makes
a student project on *counting* a natural sequel. To continue (material
about Binary and other number systems used by computers)
please click
Computer-Numbers.
To learn how computers use numbers to present colors visually please click
Color-Numbers.

In a computer message Arvind Viswanathan stated a riddle for reasoning
that applies binary representation of truth.

Your friend is trapped in a "death chamber" that has two buttons on it. There
are two robots outside the chamber. One of the robots always tells the truth
and the other robot always lies. You may ask ONE question of either of the
robots in order to free your friend. What question do you ask? To see a
solution please click Button.