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.

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))
}