Convert a number from base36 to base16 (hexadecimal) numeral.

base36_to_hex.bash

#!/bin/bash

# base36_to_hex.bash: convert a number from base36 to base16 (hexadecimal) numeral.
# Examples: 
# $ bash base36_to_hex.bash ZYXWVTSRQPONMLKJIHGFEDCBA9876543210

declare STRING_BASE36_INPUT="$1"
declare -i -r FROM_BASE=36
declare -i -r DIVISOR=16
declare dividend=${STRING_BASE36_INPUT}
declare base16_digits=""
declare string_of_4digits_numbers=""
declare -i remainder=0
declare quotient=""
declare -i subdividend=0
declare quotient_digit=""

for (( i=0; i<${#STRING_BASE36_INPUT}; i++)); do
      printf -v string_of_4digits_numbers "%s%04d" "${string_of_4digits_numbers}" $(( 36#${STRING_BASE36_INPUT:i:1} ))
done

declare dividend=${string_of_4digits_numbers}

while (( ${#dividend} >= ${#DIVISOR} )); do
  for (( position=0; position<${#dividend}; position+=4 )); do
      subdividend=$(( ${remainder} * ${FROM_BASE} + 10#${dividend:${position}:4} ))
      if [ "${quotient:0:4}" = "0000" ]; then
        printf -v quotient "%04d" $(( 10#${subdividend}/${DIVISOR} ))
      else
        printf -v quotient_digit "%04d" $(( 10#${subdividend}/${DIVISOR} ))
        printf -v quotient "%s%s" "${quotient}" "${quotient_digit}"
      fi
      remainder=$(( 10#${subdividend}%${DIVISOR} ))
  done
  printf -v base16_digits "%01X%s" "${remainder}" "${base16_digits}"
  if [ "${quotient}" = "0000" ]; then
    break
  fi
  dividend=${quotient}
  quotient=""
  remainder=0
done

for (( position=${#base16_digits}; position < $(( 256/8*2 )); position+=1 )); do
  base16_digits="0${base16_digits}"
done  

printf "%s\n" "${base16_digits}"