<CENTER> <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.