Bash integer comparison

This script works!

#/bin/bash
if [[ ( "$#" < 1 ) || ( !( "$1" == 1 ) && !( "$1" == 0 ) ) ]] ; then
    echo this script requires a 1 or 0 as first parameter.
else
    echo "first parameter is $1"
    xinput set-prop 12 "Device Enabled" $0
fi

But this also works, and in addition keeps the logic of the OP, since the question is about calculations. Here it is with only arithmetic expressions:

#/bin/bash
if (( $# )) && (( $1 == 0 || $1 == 1 )); then
    echo "first parameter is $1"
    xinput set-prop 12 "Device Enabled" $0
else
    echo this script requires a 1 or 0 as first parameter.
fi

The output is the same¹:

$ ./tmp.sh 
this script requires a 1 or 0 as first parameter.

$ ./tmp.sh 0
first parameter is 0

$ ./tmp.sh 1
first parameter is 1

$ ./tmp.sh 2
this script requires a 1 or 0 as first parameter.

_{[1] the second fails if the first argument is a string}