How to use recursion in Bash? Example: producing all {0..1} combinations of a given length.

bin.sh

#!/bin/bash
# Produces all {0..1} combinations of a given length
#
# This program is provided AS-IS with the sole purpose of
# demonstrating the use of functions and recursion in Bash
#
# Usage:
#
# sh$ ./bin.sh 3
# 000
# 001
# 010
# 011
# 100
# 101
# 110
# 111

run() {
    # usage: run count
    local count=$1

    if [[ $count -gt 0 ]]; then
        run $((count-1)) | while read head; do
            for tail in {0..1}; do
                echo "${head}${tail}"
            done
        done
    else
        echo
    fi
}

# Parameter validation left as an exercice
# ;)

run $1