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DigitSum
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DigitSum

New in 14

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gives the sum of the decimal digits in the integer n.

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DigitSum[n,b]

gives the sum of the base b digits in the integer n.

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DigitSum[n,b,k]

gives the sum of the first k base b digits in the integer n.

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DigitSum[n,b,-k]

gives the sum of the last k base b digits in the integer n.

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DigitSum[n,MixedRadix[blist]]

uses the mixed radix with list of bases blist.

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

Find the sum of the decimal digits in :

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-ruupcq
Out[1]=1

Find the sum of the binary digits in :

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-cfp0m9
Out[1]=1

Find the digit sum in a mixed radix system:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-otn38h
Out[1]=1

Scope  (8)Survey of the scope of standard use cases

Compute for large numbers:

In[9]:=9
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https://wolfram.com/xid/0bdpl07fe-bx2jiu
Out[9]=9

Use a base larger than 10:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-ixvfu2
Out[1]=1

DigitSum threads over lists:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-w7f2d8
Out[1]=1

Find the digit sum of 7 in different bases:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-7amg26
Out[1]=1

Sum only the first 4 digits:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-8udmv8
Out[1]=1

Sum only the last 4 digits:

In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-ivp7ku
Out[2]=2

Find digit sums using a MixedRadix specification:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-nrkbg0
Out[1]=1

Sum only the last 2 digits:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-2vnye
Out[1]=1

Exact values are generated at integers:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-20lxp
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

Plot the sum of the digits in the first 100 positive integers:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-3861e7
Out[1]=1

Properties & Relations  (9)Properties of the function, and connections to other functions

Use IntegerDigits to compute DigitSum:

In[6]:=6
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https://wolfram.com/xid/0bdpl07fe-n8mhqv
Out[6]=6
In[7]:=7
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https://wolfram.com/xid/0bdpl07fe-bcjear
Out[7]=7

Use HammingDistance to compute DigitSum in binary:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-f39aoi
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-j11muw
Out[2]=2

DigitSum[n,b,-k] gives 0 when k is less than or equal to IntegerExponent[n,b]:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-k77b2e
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-s0uzwr
Out[2]=2

In particular, DigitSum[0,b,k] is always 0:

In[3]:=3
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https://wolfram.com/xid/0bdpl07fe-rx9tac
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0bdpl07fe-lj5jjx
Out[4]=4

Use DigitCount to compute DigitSum in binary:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-0wii76
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-doqxgz
Out[2]=2

Use DigitCount to compute DigitSum in any base:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-weh4dn
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-phbev
Out[2]=2

IntegerLength and DigitSum give for in base :

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-ke274n
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-0vchdo
Out[2]=2

DigitSum[n,b,k] is equivalent to DigitSum[n,b] when k is greater than the integer length of n in base b:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-m2jxd2
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-h7ey9p
Out[2]=2

DigitSum gives the same result for n and IntegerReverse[n,b]:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-eip8oo
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bdpl07fe-2xik3u
Out[2]=2

The sign is ignored:

In[1]:=1
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https://wolfram.com/xid/0bdpl07fe-v8pvfm
Out[1]=1
Wolfram Research (2024), DigitSum, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitSum.html.
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Wolfram Research (2024), DigitSum, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitSum.html.

Text

Wolfram Research (2024), DigitSum, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitSum.html.

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Wolfram Research (2024), DigitSum, Wolfram Language function, https://reference.wolfram.com/language/ref/DigitSum.html.

CMS

Wolfram Language. 2024. "DigitSum." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DigitSum.html.

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Wolfram Language. 2024. "DigitSum." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DigitSum.html.

APA

Wolfram Language. (2024). DigitSum. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DigitSum.html

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Wolfram Language. (2024). DigitSum. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DigitSum.html

BibTeX

@misc{reference.wolfram_2025_digitsum, author="Wolfram Research", title="{DigitSum}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/DigitSum.html}", note=[Accessed: 26-March-2025 ]}

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@misc{reference.wolfram_2025_digitsum, author="Wolfram Research", title="{DigitSum}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/DigitSum.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_digitsum, organization={Wolfram Research}, title={DigitSum}, year={2024}, url={https://reference.wolfram.com/language/ref/DigitSum.html}, note=[Accessed: 26-March-2025 ]}

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@online{reference.wolfram_2025_digitsum, organization={Wolfram Research}, title={DigitSum}, year={2024}, url={https://reference.wolfram.com/language/ref/DigitSum.html}, note=[Accessed: 26-March-2025 ]}