Numeral systems by culture  

HinduArabic numerals  
Eastern Arabic Indian family Khmer 
Mongolian Thai Western Arabic 
East Asian numerals  
Chinese Counting rods Japanese 
Korean Suzhou 
Alphabetic numerals  
Abjad Armenian Āryabhaṭa Cyrillic 
Ge'ez Greek (Ionian) Hebrew 
Other systems  
Attic Babylonian Brahmi Egyptian Etruscan Inuit 
Mayan Quipu Roman Urnfield 
List of numeral system topics  
Positional systems by base  
Decimal (10)  
1, 2, 3, 4, 5, 8, 12, 16, 20, 60 more…  
A hexavigesimal numeral system has a base of twentysix.
Base26 may be represented by using conventional numerals for the digits 0 to 9, and then the letters A to P for the tenth to twentyfifth digits. "10" would represent 26, "11" = 27, "AB" = 271 and "NP" = 623.
Alternatively, base26 may be represented using only letters of the Latin alphabet. As there are 26 letters in English, base26 is also the highest base in which this is possible and hence utilizes every letter. 0 is represented by A, 1 = B, 2 = C ... 24 = Y, 25 = Z. Some examples: 26 = BA, 678 = BAC.
These systems are of limited practical value, although letters used in nominal or serial numbers can be thought as hexavigesimal numerals for calculation purposes if the entire alphabet is used.
The fact that 26 is a composite number and lies between two composite numbers (25 and 27) leads to many simple fractions.
B/C = A.N B/D = A.IRIRIRIR... B/E = A.GN B/F = A.FFFFFFF...
The fractions B/G, B/I, B/J, B/K, B/M, B/N, B/P, B/Q are also simple.
Any number may be converted to base26 by repeatedly dividing the number by 26. The remainders of each division will be the base26 digits from right to left (leastsignificant to mostsignificant place). For example, to convert 678 to "BAC", the first division yields 26 remainder 2, so 2 (C) is the last digit. The quotient 26 is divided again, yielding 1 remainder 0, so 0 (A) is the secondlast digit. The next quotient 1 is then divided to give 0 remainder 1, so the final digit is 1 (B). This is extensible to fractions.
This algorithm may be represented in Java to convert an integer to a base26 character string as follows:
public static String toBase26(int number){ String converted = ""; // Repeatedly divide the number by 26 and convert the // remainder into the appropriate letter. do { int remainder = number % 26; converted = (char)(remainder + 'A') + converted; number /= 26; } while (number > 0); return converted; }
This algorithm may, also, be represented in Microsoft Transact SQL to convert an integer to a base26 character string as follows
CREATE FUNCTION [dbo].[base26alpha] ( @base10int bigint ) returns varchar(max) AS begin declare @ret varchar(max) declare @remainder int declare @number bigint declare @onechar char(1) SET @ret='' SET @number=@base10int IF (@number=0) begin SET @ret='A' end else begin while (@number>0) begin SET @remainder = @number % 26 SET @onechar=char(65 + @remainder) SET @ret = @onechar + @ret SET @number=@number/26 end end RETURN @ret end
The reverse conversion is achieved by processing each base26 digit from left to right. The value of the first (leftmost) digit is multiplied by 26 and then added to the subsequent digit. If digits remain, then the cumulative sum is multiplied by 26 before adding the next digit, and so on. Note that this works for any base as long as one has the tools to perform multiplication by 26 and addition in that base. For example, to convert "BAC" to 678, B (1) is multiplied to give 26 and added to A (0) to yield 26. This is multipled to give 676 and added to C (2) to yield 678.
