(1) Radix. The term radix means the number of admissible symbols in a given number system.
The admissible symbols are all the characters (Arabic numerals, letters of the alphabet, or other
recognizable symbols) used to represent the magnitude of a numerical quantity. In several numbering
systems, some or all of the Arabic numerals are the only admissible symbols. The terms numerals, digit,
and admissible symbols can be used to mean the same in most cases. There are 10 Arabic numerals.
Thus, these symbols will work if the system radix (base) is not greater than 10. In the decimal system, all
the numerals are used; the system radix, therefore, is 10 and the radix point is known as the decimal point.
The term decimal implies 10 and no other numbering system uses a decimal point.
(2) Symbols and digits. There is no reason all the Arabic numerals must be used to make up the
admissible symbols in a numbering system. Less than all of them may be used, all of them plus others
may be used, or they may be discarded entirely and other symbols devised. In a positional numbering
system, the admissible symbols must have an order of value. This means that the difference in value
between adjacent, correctly-ordered symbols must be integral and uniform. One of the symbols must
(3) Counting. The digits or symbols in any numbering system must have an order of value.
Counting, therefore, is the process whereby the digits are advanced so that the value of an expression
increases to the next higher order; that is, advances integrally.
(a) Digit advance. Advancing a digit means replacing it with the digit of the next higher
value. In the decimal system, advancing the digit 0 means replacing it with 1; advancing 3 means
replacing it with 4; and advancing 9 means replacing it with digit 0 and carrying over a 1, thus advancing
the digit to its left. Counting may be more simply defined as the forming and expressing of successive
whole numbers. It is the same in all number systems.
(b) Significant digit. In figure 1-1 the right-most digit in each number is the least significant
digit (LSD) and the left-most digit is the most significant digit (MSD). When the number of digits in a
number increases by one during the process of counting, a breakpoint has been reached. In figure 1-1,
breakpoints are shown at the numbers 10 and 100 and 1,000. A breakpoint occurs whenever the value of
the number is an integral power of the system's radix. In the decimal system, the breakpoints are 10, 100,
1000, etc., because these are expressions of the integral powers of 10.