DigitCount

DigitCount[n,b,d]

gives the number of d digits in the base-b representation 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  (1)

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

Applications  (2)

ThueMorse sequence [more info]:

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

Introduced in 1999
 (4.0)