# Is applying a binary operator (+,-,*,/) to char arrays supported by MATLAB or just a "trick"

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Jon on 20 Jan 2022
Commented: Jon on 21 Jan 2022
I recently came across the use of the following way to obtain the individual digits of a binary number as an array of doubles, for example to get the individual binary digits of the decimal value 6:
digits = '110' - '0'
which provides the result:
digits =
1 1 0
This seemed really surprising to me, I had no idea that subtraction of character arrays was even defined.
I see digging more deeply https://www.mathworks.com/matlabcentral/answers/399557-explanation-of-num2str-x-0 that what is happening seems to be equivalent to
a = double('110')
b = double('0')
digits = a - b
where the double() creates a vector of unicodes for each character. So we have:
a =
49 49 48
b =
48
digits =
1 1 0
So I can see that if MATLAB interprets applying the binary operator, - , to two character arrays as first converting them to vectors of doubles using the unicode of each character, and then performing the subtraction on those, then it makes sense that '110' - '0' = [1 1 0].
I then experimented further and found that not only could the minus operator be applied to character arrays, but also +,*, / also give results.
In each case, MATLAB apparently first converts the pair of character arrays to vectors of doubles using the unicodes of the individual characters and then applies the operation to those. So for example:
>> '110'+'123'
ans =
98 99 99
'110'*'2'
ans =
2450 2450 2400
>> '110'/'2'
ans =
0.9800 0.9800 0.9600
My question though, is where is it documented that applying binary operators to character arrays is even defined? I couldn't seem to find this in the MATLAB documentation, but maybe I missed it.
Is this considered just a "trick" and maybe not even behavior that can be depended upon, or is it a supported operation in MATLAB?
##### 2 CommentsShowHide 1 older comment
Jon on 20 Jan 2022
Thanks all for your very interesting and informative answers to my question. There were a lot of good answers here, so it was hard to select just one to accept.

John D'Errico on 20 Jan 2022
Edited: John D'Errico on 20 Jan 2022
The plus operator has long been supported, as it applies to character arrays. I recall it existing for as long as I go back using MATLAB, which goes back to around the late 1980's, so 35 years or so.
Unary plus converts characters to their ascii equivalents.
+'abcde'
ans = 1×5
97 98 99 100 101
And numerical operations on character arrays convert them to ascii equivalent doubles first.
2 * 'ABC'
ans = 1×3
130 132 134
And I can be confident this will be the case into the future, as MathWorks does try strongly to keep features like this supported to be compatible, unless there is a compelling reason to need to change such a capability. There are huge bases of code that use this trick. So I doubt they will want to force many users to go into existing code and hack it just so they can remove an old feature.
At the same time, They MAY be preparing us for a long term eventuality where unary plus will no longer apply to character arrays, because a quick search through the docs does not show this capability. Of course, + does not do the same when applied to strings.
1 + "ABC"
ans = "1ABC"
Anyway, my guess is this feature will be supported for long after I am dead and converted to soylent green, even if it is not documented. There are other ways to convert a character array to ascii equivalents. Double may be the preferred way now:
double('abcde')
ans =
97 98 99 100 101
though I would need to think. (I am so used to just using the plus operator.)
##### 2 CommentsShowHide 1 older comment
John D'Errico on 20 Jan 2022
Sadly, I had heard that. We may want to avoid the green smoothies. :)

Matt J on 20 Jan 2022
I can't find the documentation, but binary operators in Matlab can't define themselves. It had to be deliberate.
Also, the char binary operators have been there for 40 years, so I don't think they'd dare remove them now.
Also, the same definitions are found in C\C++ and very commonly used for the kind of purposes shown in your example.

Yongjian Feng on 20 Jan 2022
Char array is a vector of chars. So you are basically doing vector operation, right?

DGM on 20 Jan 2022
Edited: DGM on 20 Jan 2022
MATLAB is a weakly-typed language; consequently, implicit type conversions tend to happen all the time. I don't know where (or if) this specific behavior is explicitly documented, although the docs for these operators mention that 'char' is a supported type.
As to whether it can be used safely, I would say yes. It's fairly routine to use this sort of approach for converting text representations of numbers into numeric vectors:
mytextnum = '01234567';
mynum = mytextnum-'0'
Or perhaps for converting text into numeric indices:
bunchofchars = '123abcXYZ';
positioninalphabet = lower(bunchofchars(isletter(bunchofchars)))-'a'+1
Note that using arithmetic operators on strings doesn't behave the same way. Addition is treated as a concatenation operator for strings.
"110"+"0"
Trying to use the other operators on a pair of strings would result in an error.
##### 2 CommentsShowHide 1 older comment
DGM on 20 Jan 2022
That's basically why I think it is confusing. Let me clarify. I don't think it's confusing that addition doesn't add strings. I think it's confusing that addition concatenates instead of throwing an error. It's been almost 15 years since I touched a language that did this, so it seems wrong to "add" words. Maybe that's just a demonstration of how quickly and thoroughly I forget things.

Paul on 20 Jan 2022
Not directly on point to the Question, but a related "feature" is that char vectors can be used to directly into index into arrays:
data = rand(1,150);
isequal(data('a'),data(double('a')))
ans = logical
1
isequal(data('abc'),data(double('abc')))
ans = logical
1
However, there is an execption for ':'
isequal(data(':'),data(double(':')))
ans = logical
0
Because indexing with ':' is the same as :
isequal(data(':'),data(:))
ans = logical
1
Jon on 21 Jan 2022
Aha! Thanks so much.

R2021b

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