The number of 1s in binary representation:

The number of 1s and 0s:

Confirm by extending the number in binary:

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

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

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:

Get them in the opposite order:

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

Elements 0 through 24 of the Thue–Morse sequence:

Compare with the answer given by ThueMorse:

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

DigitCount[n] is equivalent to DigitCount[n,10,Mod[Range[10],10]]:

DigitCount[n,b,dlist] threads over the digits in the list dlist:

DigitCount[nlist,…] threads over the digits in the list nlist:

Specify a list of numbers and a base:

For DigitCount[nlist,b,dlist,…], the result is a list of Length[nlist] lists, each of length Length[dlist]:

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]:

DigitCount[n,b] equals Values[Counts[IntegerDigits[n,b],Mod[Range[b],b]]:

By extension, this also applies to DigitCount[n] with b==10 on the right-hand side:

DigitCount[0,b,0] gives 1:

This is consistent with the behavior of IntegerDigits[0,b]:

DigitCount[n,b,{}] gives {}:

DigitCount and IntegerDigits consider 0 to consist of a single digit:

IntegerLength, by contrast, considers 0 to have no digits:

The basis argument cannot be list:

Neither can the trailing digits count argument:

Use Map to manually thread over these arguments if desired: