DigitCount

DigitCount[n,b,d]

gives the number of d digits in the base-b representation of n.

DigitCount[n,b,d,len]

gives the number of d digits in the base-b representation of the last len digits of n.

DigitCount[n,b]

gives a list of the numbers of , , …, , digits in the base-b representation of n.

DigitCount[n]

gives a list of the numbers of , , …, , digits in the base-10 representation of n.

Details

  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • DigitCount[n] is equivalent to DigitCount[n,10,Mod[Range[10],10]].

Examples

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Basic Examples  (3)

Binary representation:

Number of 1s in binary representation:

Number of 1s and 0s:

Number of each digit 1, 2, 3, ..., 0 in 100!:

Plot the number of 1s in the base-2 representation:

Scope  (2)

Count the number of each of the decimal digits in a number:

Do the same thing, explicitly specifying the base:

Count just the number of zeros:

Count the number of zeros, assuming a 9-digit number:

Count the number of digits 1 and 2 in ternary representation:

Count the number of digits 1 and 2 in the last 12 digits of the ternary representation:

Applications  (2)

Thue–Morse sequence [more info]:

Number of black cells at step t in the rule 90 cellular automaton (binomial coefficients mod 2):

Properties & Relations  (2)

DigitCount[n,b,d] is effectively Count[IntegerDigits[n,b],d]:

DigitCount[n,b,d,len] is effectively Count[PadLeft[IntegerDigits[n,b],len],d]:

Wolfram Research (1999), DigitCount, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitCount.html (updated 2025).

Text

Wolfram Research (1999), DigitCount, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitCount.html (updated 2025).

CMS

Wolfram Language. 1999. "DigitCount." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/DigitCount.html.

APA

Wolfram Language. (1999). DigitCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DigitCount.html

BibTeX

@misc{reference.wolfram_2024_digitcount, author="Wolfram Research", title="{DigitCount}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/DigitCount.html}", note=[Accessed: 20-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_digitcount, organization={Wolfram Research}, title={DigitCount}, year={2025}, url={https://reference.wolfram.com/language/ref/DigitCount.html}, note=[Accessed: 20-January-2025 ]}