How do I convert an ASCII character to its decimal (or hexadecimal) value and back?

If you have a known octal or hexadecimal value (at script-writing time), you can just use printf:

   # POSIX
   printf '\x27\047\n'

This prints two literal ' characters (27 is the hexadecimal ASCII value of the character, and 47 is the octal value) and a newline.

If you need to convert characters (or numeric ASCII values) that are not known in advance (i.e., in variables), you can use something a little more complicated:

   # POSIX
   # chr() - converts decimal value to its ASCII character representation
   # ord() - converts ASCII character to its decimal value

   chr() {
     printf \\$(printf '%03o' $1)
   }

   ord() {
     printf '%d' "'$1"
   }

   # hex() - converts ASCII character to a hexadecimal value
   # unhex() - converts a hexadecimal value to an ASCII character

   hex() {
      printf '%x' "'$1"
   }

   unhex() {
      printf \\x"$1"
   }

   # examples:

   chr $(ord A)    # -> A
   ord $(chr 65)   # -> 65

The ord function above is quite tricky.

This version of chr executes much faster than the printf version above (about 1/40 to less than 1/150 the time when run in a loop):

   chr() { echo -en "\0$(( $1 % 8 + 10 * ( $1 / 8 ) + 20 ))"; }

   for p in chr newchr; do time for i in {1..4000}; do $p 65 >/dev/null; done; done

   System1                     System2
   real    0m46.824s           real    1m33.814s
   user    0m4.624s            user    0m8.540s
   sys     0m33.290s           sys     1m23.978s

   real    0m1.340s            real    0m0.512s
   user    0m1.096s            user    0m0.389s
   sys     0m0.124s            sys     0m0.096s

This version is faster as it executes without a subshell, it seems to only work strictly on ascii chars <127 while the printf version is happy with chars up to 255 and also for only a subset of ascii ie >64 decimal. Some versions avoiding a subshell:

oldchr () {  printf \\$(printf '%03o' $1) ;}

#posix
chr () {
    set -- $(($1 / 64)) $(($1 % 64))
    set -- $1  $(($2 / 8)) $(($2 % 8))
    printf \\"${1}${2}${3}"
}

#bash only
chr_bash () {
    local temp
    printf -v temp  '%03o' $1
    printf \\$temp
}

#test
for i in {1..255} ;do [[ "$(oldchr $i)" = "$(chr $i)" ]] || echo $i;done
for i in {1..255} ;do [[ "$(oldchr $i)" = "$(chr_bash $i)" ]] || echo $i;done
for p in oldchr chr chr_bash; do echo $p:;time for i in {1..4000}; do $p 65 >/dev/null; done; done

the timings:

$ bash  chr
oldchr:

real    0m14.350s
user    0m5.004s
sys     0m9.248s
chr:

real    0m0.422s
user    0m0.059s
sys     0m0.216s
chr_bash:

real    0m0.400s
user    0m0.042s
sys     0m0.189s

Yet another version probably faster:

chr () {
    printf \\$(($1/64*100+$1%64/8*10+$1%8))
}