IntegerString

IntegerString[n]

gives a string consisting of the decimal digits in the integer n.

IntegerString[n,b]

gives a string consisting of the base-b digits in the integer n.

IntegerString[n,b,len]

pads the string on the left with zero digits to give a string of length len.

IntegerString[n,MixedRadix[blist]]

uses the mixed radix with a list of bases blist.

IntegerString[n,"numsys"]

gives the numeral form of n based on the numeric system defined by "numsys".

Details

  • The maximum allowed base is 36. For bases larger than 10, additional digits are chosen from the letters az.
  • IntegerString[n] discards the sign of n.
  • If len is less than the number of digits in n, then the len least significant digits are returned.
  • In IntegerString[n,"numsys"], possible human-use numeric systems "numsys" include:
  • "Arabic"Arabic numerals
    "ArabicExtended"extended Arabic numerals
    "Armenian"Armenian numerals
    "ArmenianLower"lowercase Armenian numerals
    "Bengali"Bengali numerals
    "Chinese"Chinese numerals
    "Devanagari"Devanagari numerals
    "Ethiopic"Ethiopic numerals
    "Georgian"Georgian numerals
    "Greek"Greek numerals
    "GreekLower"lowercase Greek numerals
    "Gurmukhi"Gurmukhi numerals used in Punjabi language
    "Hebrew"Hebrew numerals
    "Japanese"Japanese numerals
    "JapaneseFinancial"Japanese numerals used for financial purposes
    "Kannada"Kannada numerals
    "KayahLi"Kayah Li numerals
    "Malayalam"Malayalam numerals
    "N'ko"N'ko numerals
    "Oriya"Oriya, also known as Odia, numerals
    "Roman"Roman numerals
    "RomanVariant"Roman numerals that use only Unicode characters
    "RomanLower"lowercase Roman numerals
    "SimplifiedChinese"Simplified Chinese numerals
    "SimplifiedChineseFinancial"Simplified Chinese numerals used for financial purposes
    "Tai"Tai numerals
    "Tamil"Tamil numerals
    "TamilDecimal"base-10 Tamil numerals
    "Tao"Tao, also known as Yami, numerals
    "Telugu"Telugu numerals
    "Thai"Thai numerals
    "Tibetan"Tibetan numerals
    "TraditionalChinese"numerals used in Traditional Chinese
    "TraditionalChineseCalendar"numerals used in Traditional Chinese calendars
    "TraditionalChineseDecimal"base-10 Traditional Chinese numerals
    "TraditionalChineseFinancial"Traditional Chinese numerals used for financial purposes
  • Possible machine-use numeric systems include:
  • "Base58"base-58 digits with Bitcoin encoding alphabet
    "Base64"base-64 digits with Base64 encoding alphabet

Examples

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Basic Examples  (4)

Convert to binary, giving the result as a string:

Convert to Roman numerals:

Convert to Japanese financial numerals:

Convert to a base-64 representation:

Scope  (4)

In base 16, a through f are used as digits:

Use a MixedRadix specification:

Find only the last 2 characters:

Use a numsys as specification:

Generalizations & Extensions  (1)

The maximum base of 36 uses letters a through z:

Properties & Relations  (4)

ToUpperCase converts to uppercase letters:

FromDigits may be used as the inverse of IntegerString:

Not all numeric systems are supported by FromDigits:

This is the largest number representable in a mixed radix system with bases 1 36:

Use the "Base64" alphabet to express an integer in powers of 64:

Compare with:

Possible Issues  (1)

Some numeric systems are defined only in a limited numeric range:

Neat Examples  (1)

Show a single number in successive bases from 2 to 36:

Introduced in 2007
 (6.0)
 |
Updated in 2015
 (10.1)
2017
 (11.1)
2018
 (11.3)
2019
 (12.0)
2020
 (12.1)