为什么此代码可以将十六进制转换为十进制

Question

This code will convert one hexadecimal digit into a decimal value.

int value;
// ch is a char variable holding a hexadecimal digit
if (isxdigit(ch))
    if (isdigit(ch))
        value = ch - '0';
    else
        value = tolower(ch) - 'a' + 10;
else
    fprintf(stderr, "%c is not a valid hex digit", ch);

I don't fully understand how it works though. I can see that different things are subtracted from the char variable depending on whether it is a number or a letter. I can understand the part where a number gets converted, but I don't understand why 10 has to be added to the value when the character is a letter.

Answer 1

The subtraction of tolower(ch) - 'a' will map the character to a number in the range 0..5 for the letters a..f. However, the (decimal) value of the hexadecimal digit a ₁₆ is 10 ₁₀ , so to move the range back up to 10..15 where it needs to be, 10 is added.

Perhaps this helps:

+---------+------------+-----------------+-------------+
Character | Subtracted | Resulting value | Digit value |
+---------+------------+-----------------+-------------+
|   '0'   |     '0'    |       0         |       0     |
|   '1'   |     '0'    |       1         |       1     |
|   '2'   |     '0'    |       2         |       2     |
|   '3'   |     '0'    |       3         |       3     |
|   '4'   |     '0'    |       4         |       4     |
|   '5'   |     '0'    |       5         |       5     |
|   '6'   |     '0'    |       6         |       6     |
|   '7'   |     '0'    |       7         |       7     |
|   '8'   |     '0'    |       8         |       8     |
|   '9'   |     '0'    |       9         |       9     |
|   'a'   |     'a'    |       0         |      10     |
|   'b'   |     'a'    |       1         |      11     |
|   'c'   |     'a'    |       2         |      12     |
|   'd'   |     'a'    |       3         |      13     |
|   'e'   |     'a'    |       4         |      14     |
|   'f'   |     'a'    |       5         |      15     |
+---------+------------+-----------------+-------------+

Notice how the "resulting value" column resets back to 0 at 'a', which is not where it needs to be according to the final "digit value" column, which shows each hexadecimal digit's value in decimal.

Answer 2

The expression ch - '0' works because in C "the value of each character after 0 ... shall be one greater than the value of the previous" ( C99 section 5.2.1).

So, for example, the value of the character '3' is 3 greater than the value of '0' , so when you subtract these two values, you get the integer 3.

The expression tolower(ch) - 'a' + 10 works by luck, because, except for the above constraint for digits, all values of characters are implementation-defined.

So when you subtract 'c' - 'a' you get 2 (and, adding 10, you get 12 – the correct value of that digit), because most computers work in ASCII or EBCDIC. But when you run this program on the DS9K, you might get −42.

To be truly portable you would need to compare ch to each of the six letters in turn. That's why some systems provide a digittoint() function.