bash function to output set bits in a decimal integer

Doing some redesign of our webserver and wrote a quick shell function to give me the bitwise properties of a given integer. enjoy if you have any use for it. ./Stevo

 #!/bin/bash

 function bitwise {
    val=$1
    if [[ ${val} -le $((2**8)) ]]; then
       max=8
    elif [[ ${val} -le $((2**16)) ]]; then
       max=16
    elif [[ ${val} -le $((2**32)) ]]; then
       max=32
    elif [[ ${val} -le $((2**64)) ]]; then
       max=64
    fi
    printf "binary: %0${max}dn" $(echo "obase=2; ${val}" | bc -l)
    for i in $(seq 1 ${max}); do
    if test  $((${val} & $(((1<<${i} - 1))))) -gt 0; then
       echo "bit:${i} set"
    fi
    done
 }

output:

stevenh@lnx:~$ bitwise 500
binary: 0000000111110100
bit:3 set
bit:5 set
bit:6 set
bit:7 set
bit:8 set
bit:9 set