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IntegerString

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

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 n; digit values 10 to 35 use the letters a-z.
IntegerString[n, b, len] pads the string on the left with zero digits to give a string of length len; if len is less than the number of digits in n, the len least-significant digits are returned.
The maximum allowed base is 36; the sign of n is discarded.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= IntegerString[17651, 2]
Out[1]= "100010011110011"

In[2]:= IntegerString[50!, 16]
Out[2]= "49eebc961ed279b02b1ef4f28d19a84f5973a1d2c7800000000000"

In[3]:= IntegerString[50!, 36]
Out[3]= "4q7eyp9zizmtqt0648txt4fm720cc1s00000000000"

In[4]:= IntegerString[Range[0, 7], 2, 3]
Out[4]= {"000", "001", "010", "011", "100", "101", "110", "111"}

In[5]:= IntegerString[12345, 10, 3]
Out[5]= "345"

In[1]:= IntegerString[]
Out[1]= IntegerString[]

In[1]:= IntegerString[11.3423]
Out[1]= IntegerString[11.3423]

In[1]:= IntegerString[10, 50]
Out[1]= IntegerString[10, 50]

Implementation notes

builtin_integerstring renders |n| as a base-b digit string (default 10, optional left-padded length). It calls GMP's mpz_get_str, which emits '0'..'9','a'..'z' for bases up to 62; the base is capped at 36 to match Mathematica's surface convention. A length argument left-pads with '0' or keeps only the low-order digits. Sign is discarded; IntegerString[0] is "0". Validates arity (IntegerString::argb), numeric non-integer n (::int), base in [2, 36] (::basf), and non-negative machine length (::intnn); registered Listable so list inputs thread.

  • Protected, Listable. Threads element-wise over a list of integers in

Attributes: Listable, Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= IntegerString[255, 16]
Out[1]= "ff"

In[1]:= IntegerString[255, 2]
Out[1]= "11111111"

In[2]:= IntegerString[42, 2, 16]
Out[2]= "0000000000101010"

In[1]:= IntegerString[123456789, 36]
Out[1]= "21i3v9"

In[1]:= IntegerString[3^50, 16]
Out[1]= "980553f0db2fd09de3c9"

Notes

IntegerString[n, b] renders n as a base-b string, using the digits 0-9 and then the letters a-z for values 10 through 35 (so the maximum base is 36). A third argument left-pads with zeros to a fixed width. Because the conversion runs at arbitrary precision, large numbers like 3^50 are formatted exactly in hexadecimal. The sign of n is discarded.