DigitCount

Counts of each digit (1 through 9, then 0) occurring in n, base 10 by default.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageDigitCount✓↗

DigitCount(n)counts of each digit 1-9 then 0, base 10.

DigitCount(n, base)counts of each digit in the given base, highest digit value first.

DigitCount(n, base, digit)count of just one digit value.

DigitCount(n, base, digit(s), width)counted over exactly width digits, padded or truncated to fit.

Typed signatures

Type	Package	Applies
(integer, integer?, integer?) -> integer | list<integer>	compute-engine	always
(integer, integer?, (integer | list<integer>)?, integer?) -> integer | list<integer>	numeralsreplaces compute-engine	always

Domain: Numeral systems

Details

• Equivalent to tallying IntegerDigits(n, base) bucket by bucket.
• The default base-10 form orders counts 1 through 9, then 0 last.
• The 3-argument form isolates the count of a single digit value.
• Trailing zeros count individually -- 122000 has three trailing 0 digits, not a single "trailing zeros" tally.

Examples

Basic #

live ↗

In$\mathrm{DigitCount}(2\,147)$Out$\bigl\lbrack1, 1, 0, 1, 0, 0, 1, 0, 0, 0\bigr\rbrack$

In base 2, counts of digit 1 then digit 0

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In$\mathrm{DigitCount}(2\,147, 2)$Out$\bigl\lbrack5, 7\bigr\rbrack$

$2147 = 100001100011_2$ has five 1 bits

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In$\mathrm{DigitCount}(2\,147, 2, 1)$Out$5$

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In$\mathrm{DigitCount}(122\,000)$Out$\bigl\lbrack1, 2, 0, 0, 0, 0, 0, 0, 0, 3\bigr\rbrack$

Scope #

an explicit base 10 is the default

live ↗

In$\mathrm{DigitCount}(122\,000, 10)$Out$\bigl\lbrack1, 2, 0, 0, 0, 0, 0, 0, 0, 3\bigr\rbrack$

the digits of $100!$, 30 of them zeros

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In$\mathrm{DigitCount}(100!)$Out$\bigl\lbrack15, 19, 10, 10, 14, 19, 7, 14, 20, 30\bigr\rbrack$

a width counts padding zeros too: $000122000$ has six

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In$\mathrm{DigitCount}(122\,000, 10, 0, 9)$Out$6$

a list of digit values gives one count each

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In$\mathrm{DigitCount}(242\,442\,422, 3, \bigl\lbrack1, 2\bigr\rbrack)$Out$\bigl\lbrack6, 7\bigr\rbrack$

counts over the 12 least-significant base-3 digits

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In$\mathrm{DigitCount}(242\,442\,422, 3, \bigl\lbrack1, 2\bigr\rbrack, 12)$Out$\bigl\lbrack4, 4\bigr\rbrack$

Threads element-wise over a list, as Wolfram's Listable heads do

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In$\mathrm{DigitCount}(\bigl\lbrack23, 45\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack0, 1, 1, 0, 0, 0, 0, 0, 0, 0\bigr\rbrack, \bigl\lbrack0, 0, 0, 1, 1, 0, 0, 0, 0, 0\bigr\rbrack\bigr\rbrack$

Applications #

The 3-argument form isolates a single digit's count

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In$\mathrm{DigitCount}(2\,147, 10, 1)$Out$1$

Properties #

Single-digit form matches counting that digit in the digit list

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In$\mathrm{DigitCount}(242\,442\,422, 3, 0)=\mathrm{Count}(\mathrm{IntegerDigits}(242\,442\,422, 3), 0)$Out$\mathrm{True}$

A fourth argument counts leading zeros in a fixed-width field

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In$\mathrm{DigitCount}(242\,442\,422, 3, 0, 20)=\mathrm{Count}(\mathrm{PadLeft}(\mathrm{IntegerDigits}(242\,442\,422, 3), 20), 0)$Out$\mathrm{True}$

Result lists counts for digits $1,\dots,b-1$ then $0$; zero is a single $0$

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In$\mathrm{DigitCount}(0, 2)$Out$\bigl\lbrack0, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

One binary digit $1$, no zeros

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In$\mathrm{DigitCount}(1, 2)$Out$\bigl\lbrack1, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$10_2$: one of each

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In$\mathrm{DigitCount}(2, 2)$Out$\bigl\lbrack1, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$11_2$ has two ones

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In$\mathrm{DigitCount}(3, 2)$Out$\bigl\lbrack2, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$100_2$: one 1 and two 0s

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In$\mathrm{DigitCount}(4, 2)$Out$\bigl\lbrack1, 2\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$101_2$ has two ones and one zero

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In$\mathrm{DigitCount}(5, 2)$Out$\bigl\lbrack2, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$110_2$ has the same counts as $101_2$

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In$\mathrm{DigitCount}(6, 2)$Out$\bigl\lbrack2, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$111_2$ has no zeros

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In$\mathrm{DigitCount}(7, 2)$Out$\bigl\lbrack3, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$1000_2$: a power of two has one 1

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In$\mathrm{DigitCount}(8, 2)$Out$\bigl\lbrack1, 3\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$1001_2$ balances ones and zeros

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In$\mathrm{DigitCount}(9, 2)$Out$\bigl\lbrack2, 2\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$1010_2$ also two of each

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In$\mathrm{DigitCount}(10, 2)$Out$\bigl\lbrack2, 2\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

Zero in base 3, counted under the final slot for digit $0$

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In$\mathrm{DigitCount}(0, 3)$Out$\bigl\lbrack0, 0, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

Count vector runs over digits $1,2,0$

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In$\mathrm{DigitCount}(1, 3)$Out$\bigl\lbrack1, 0, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

A lone digit 2 shows in the middle slot

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In$\mathrm{DigitCount}(2, 3)$Out$\bigl\lbrack0, 1, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$10_3$: a one and a zero

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In$\mathrm{DigitCount}(3, 3)$Out$\bigl\lbrack1, 0, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$11_3$ has two ones

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In$\mathrm{DigitCount}(4, 3)$Out$\bigl\lbrack2, 0, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$12_3$: one of digit 1, one of digit 2

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In$\mathrm{DigitCount}(5, 3)$Out$\bigl\lbrack1, 1, 0\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

$20_3$: a two and a zero

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In$\mathrm{DigitCount}(6, 3)$Out$\bigl\lbrack0, 1, 1\bigr\rbrack$

Known value · Wolfram MathematicalFunctionData, DigitCount

Possible issues #

Three trailing zeros, not four: $122000$ has digits $1,2,2,0,0,0$

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In$\mathrm{DigitCount}(122\,000, 10, 0)$Out$3$

0 has one digit, a zero

live ↗

In$\mathrm{DigitCount}(0)$Out$\bigl\lbrack0, 0, 0, 0, 0, 0, 0, 0, 0, 1\bigr\rbrack$

About

Examples	33
Checked against	Wolfram Language 33 agree
Crosswalk	Wolfram Language

See also: IntegerDigits, DigitSum