# FromDigits

FromDigits[list]

constructs an integer from the list of its decimal digits.

FromDigits[list,b]

takes the digits to be given in base b.

uses the mixed radix with list of bases blist.

FromDigits["string"]

constructs an integer from a string of digits.

FromDigits["string","Roman"]

constructs an integer from Roman numerals.

# Details • FromDigits is effectively the inverse of IntegerDigits and IntegerString.
• FromDigits[{list,n},b] takes n to be an exponent, while FromDigits[{{a1,a2,,{rep}},n},b] takes rep to be repeated, so that FromDigits can also be used as the inverse of RealDigits.
• Since discards the sign of n, is Abs[n], not just n. »
• The digits in list and the base b need not be positive integers, and can be any expression. »
• If Indeterminate appears in list, it is assumed to signify unknown digits beyond the precision of an approximate real number. »
• FromDigits["string",b] takes the digits in "string" to be given in base b.
• In FromDigits["string",b], digits above 9 can be represented by letters az or AZ.

# Examples

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## Basic Examples(5)

Construct a number from its base-10 digits:

Base-2 digits:

Construct a number from digits given as string:

Construct a number from digits base 2:

Construct a number from digits in a mixed radix system:

## Scope(5)

Use symbolic digits and base:

Digits larger than the base are "carried":

Reconstruct a rational number from recurring digits:

Reconstruct a number from its digits in a mixed radix system:

Convert from Roman numerals:

## Generalizations & Extensions(1)

Construct a number with limited precision:

## Applications(3)

Find the number with recurring digits 123:

Find numbers with successive recurring binary digit sequences:

## Properties & Relations(1)

Reconstruct a number of seconds from a list {days,hours,minutes,seconds}:

It can also be obtained with NumberCompose:

Perform the same computation using Quantity objects:

## Possible Issues(3)

IntegerDigits drops the sign:

Without a base specified, the characters are interpreted as extensions of base-10 digits:

If no base is specified, the multicharacter strings are converted using base 10: