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IntegerDigits

Status: Stable

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

Description

IntegerDigits[n] gives a list of the decimal digits in the integer n.
IntegerDigits[n, b] gives a list of the base b digits in the integer n.
IntegerDigits[n, b, len] pads the list on the left with zeros to give a list of length len; if n has more than len base-b digits, the last len least-significant digits are returned.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= IntegerDigits[58127]
Out[1]= {5, 8, 1, 2, 7}

In[2]:= IntegerDigits[58127, 16]
Out[2]= {14, 3, 0, 15}

In[3]:= IntegerDigits[Range[0, 7], 2, 3]
Out[3]= {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}}

In[4]:= IntegerDigits[6345354, 10, 4]
Out[4]= {5, 3, 5, 4}

Implementation notes

builtin_integerdigits returns the base-b digit list of |n| (default base 10, optional fixed length). It coerces n and base to GMP, then peels least-significant digits with a mpz_tdiv_qr divmod loop into a geometrically-grown mpz_t buffer (O(log_b |n|)), and emits them most-significant-first into a List. A length argument left-pads with zeros (or keeps only the low-order digits if shorter). Validates arity (IntegerDigits::argb), non-integer numeric n (::int), base >= 2 (::ibase), and a non-negative machine-sized length (::intnn); symbolic n flows through as NULL.

  • Protected, Listable. Threading distributes element-wise over a list

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]:= IntegerDigits[12345]
Out[1]= {1, 2, 3, 4, 5}

In[1]:= IntegerDigits[255, 16]
Out[1]= {15, 15}

In[2]:= IntegerDigits[255, 2]
Out[2]= {1, 1, 1, 1, 1, 1, 1, 1}

In[3]:= IntegerDigits[5, 2, 8]
Out[3]= {0, 0, 0, 0, 0, 1, 0, 1}

In[1]:= Total[IntegerDigits[2^100]]
Out[1]= 115

In[1]:= IntegerDigits[100!, 10][[1 ;; 5]]
Out[1]= {9, 3, 3, 2, 6}

Notes

IntegerDigits[n] returns the decimal digits of n most-significant first; IntegerDigits[n, b] works in base b, and a third argument left-pads (or truncates to the least-significant) to a fixed length. Because Mathilda carries arbitrary-precision integers, the digit list of a giant number such as 2^100 or 100! is exact — handy for digit-sum problems and divisibility tricks. The sign of n is ignored.