What Boolean logic process could be used to convert the binary form of all decimal digits to the hexadecimal representation of its ASCII character ex 00001000 converted to 00111000 OR 8 converted?

Answer 1

You don't need boolean logic, you simply add 0x30 (48 decimal) to the digit to obtain its ASCII character value. The digits 0 to 9 have ASCII codes 0x30 to 0x39 (48 to 57 decimal), respectively. Therefore adding 48 to any value in the range 0 to 9 will reveal the character code for that value.

Thus the following are all equivalent to obtaining the ASCII character code for the digit '8':

8 + 48 = 56

8 + 0x30 = 56

8 + '0' = 56

56 decimal is 0x38 hexadecimal, or 00111000 in binary.

Note that some programming languages may not support all forms of the above. The last form (8 + '0') is the preferred method where supported as it makes it perfectly clear what the intent is: to add a value to the ASCII code '0'.

Most programming languages permit you to format the underlying binary value as decimal or hexadecimal for printing purposes, so there's usually no need to manually convert to hexadecimal. E.g, for a given value, the following will print the value in both hex and decimal:

printf("Decimal: %d, Hex: %x\n", value, value );

In the interest of completeness, the algorithm for converting any given decimal value to its hex equivalent is as follows (in pseudocode):

1. Let the output string be an empty string.
   1. Let ch be value % 16 (modus, or remainder of division).
   2. If ch is less than 10, add 48 to ch, otherwise add 65 to ch.*
   3. Prepend ch to the output string.
   4. Let value be value / 16.
2. While the value is non-zero...
3. end while
4. Print the string.**

*65 is the ASCII character code for 'A'. For lower case, add 97 instead (character code for 'a').

**You must prepend characters. If you append them, you must reverse the string before printing.