Why does subtracting '0' from an array of char appear to convert it to a numerical double.

X = '11231101' is an array of char

X - '0' seems to convert it to an array of double (I have seen coding doing this)

How is this working and where can I find an explanation of it. It looks very useful, but I want to understand it before I use it for real.

[Stephen23]

"How is this working and where can I find an explanation of it."

It simply subtracts the character codes of each character. Unicode character codes are briefly introduced here:

https://www.mathworks.com/help/matlab/matlab_prog/unicode-and-ascii-values.html

Like everything else on your computer, text is really just long lists of numbers, so there is no reason why they cannot be subtracted, multiplied, added, etc.

Answer 1

[Rik]

The minus function is not really defined for char, so the operands need to be converted to a datatype that is supported.

Since char is a UTF-16 encoding, subtracting '0' from a char vector will convert the array to double, essentially converting all characters to their Unicode representation. Since those were developed by people to make sense, they just happen to be in increasing order.

double('0123456789')

ans = 1×10

48 49 50 51 52 53 54 55 56 57

double('0')

ans = 48

double('0123456789')-double('0')

ans = 1×10

0 1 2 3 4 5 6 7 8 9

Thus, subtracting 48 from the UTF-16 encoded Unicode value will give you the equivalent numbers.

[Chris Joyce]

Thank you

[Walter Roberson]

The very early electronic character sets had the characters in an order designed to reduce wear and tear. Once that stopped being the primary concern, people started arranging letters and numbers mostly consecutively, typically 0 through 9. However, IBM, building on its history of card-driven automation, chose to order its Binary Coded Decimal (BCD) as 1 to 9 followed by 0; certainly by the time they designed EBCDIC that was the case. EBCDIC was not widely adopted.

[Walter Roberson]

Notice that if you subtract '0' from characters for digits, then provided that the underlying character set has the digits in consecutive order, then it does not matter where in the order the list is, the calculation will come out right. All modern character sets encode '0' as the 49th character, decimal value 48, but if it had happened to be placed at (say) position 100, then it would not have mattered for the purpose of subtracting '0' to get the relative offset.

The property does not hold for the representation of all languages

rei  = '零';        %zero
ichi = '一';        %one
san = '二';         %two

san - ichi

ans = 140

san - rei

ans = -18538

[Rik]

It doesn't even hold for 'normal' arabic numerals if you look at superscript (because 123 were introduced at an earlier stage):

low='₀₁₂₃₄₅₆₇₈₉';low_zero=low(1);
sup='⁰¹²³⁴⁵⁶⁷⁸⁹';sup_zero=sup(1);
low-low_zero

ans = 1×10

0 1 2 3 4 5 6 7 8 9

sup-sup_zero

ans = 1×10

0 -8119 -8126 -8125 4 5 6 7 8 9

[Walter Roberson]

Good point, @Rik