Why does nested for-loop generate wrong numbers?

Question

What i wanted to do

I wanted to create subfolders and within some new subfolders.Their names only contain the numbers 0 and 1. I used nested for-loops for this. Somehow the script generates folders with 3,4,5,6,7,8,9. I cannot find the problem or a solution.

What i already did

I already implemented an echo in every loop which shows the content of the different variables, which was always 0 or 1. Also I put a if statement in which resets a variable back to 0 after the loop is finished. Since echo shows the right content there was no need for a if statement.

DIR=/home/$USER/testdaten
mkdir /home/$USER/testdaten

for a in {0..1}; do
    mkdir $DIR/$( printf %01d $a)
    echo $DIR/$( printf %01d "$a")
    echo $a $b $c $d
    for b in {0..1}; do
        mkdir $DIR/$a/$( printf %02d $a$b)
        echo $DIR/$a/$( printf %02d $a$b)
        echo $a $b $c $d
        for c in {0..1}; do
            mkdir $DIR/$a/$a$b/$( printf %03d $a$b$c)
            echo $DIR/$a/$a$b/$( printf %03d $a$b$c)
            echo $a $b $c $d
            for d in {0..1}; do
                mkdir $DIR/$a/$a$b/$a$b$c/$( printf %04d $a$b$c$d)
                echo $DIR/$a/$a$b/$a$b$c/$( printf %04d $a$b$c$d)      
                echo $a $b $c $d 
            done
        done
    done
done


alternative:

for ((a=0; a<=1; a++)); do
mkdir $DIR/$( printf %01d "$a")
    for ((b=0; b<=1; b++)); do
        mkdir $DIR/$a/$( printf %02d "$a$b")
        for ((c=0; c<=1; c++)); do
            mkdir $DIR/$a/$a$b/$( printf %03d "$a$b$c")
            for ((e=0; e<=1; e++)); do
                mkdir $DIR/$a/$a$b/$a$b$c/$( printf %04d "$a$b$c$e")       
            done
        done
    done
done

/home/$USER/testdaten/0
0
/home/$USER/testdaten/0/00
0 0
/home/$USER/testdaten/0/00/000
0 0 0
/home/$USER/testdaten/0/00/000/0000
0 0 0 0
/home/$USER/testdaten/0/00/000/0001
0 0 0 1
/home/$USER/testdaten/0/00/001
0 0 1 1
/home/$USER/testdaten/0/00/001/0008
0 0 1 0
/home/$USER/testdaten/0/00/001/0009
0 0 1 1
/home/$USER/testdaten/0/01
0 1 1 1
/home/$USER/testdaten/0/01/008
0 1 0 1
mkdir: das Verzeichnis »/home/$USER/testdaten/0/01/010/0064“ kann nicht angelegt werden: Datei oder Verzeichnis nicht gefunden
/home/$USER/testdaten/0/01/010/0064
0 1 0 0
mkdir: das Verzeichnis »/home/$USER/testdaten/0/01/010/0065“ kann nicht angelegt werden: Datei oder Verzeichnis nicht gefunden
/home/$USER/testdaten/0/01/010/0065
0 1 0 1
/home/e$USER/testdaten/0/01/009
0 1 1 1
mkdir: das Verzeichnis »/home/$USER/testdaten/0/01/011/0072“ kann nicht angelegt werden: Datei oder Verzeichnis nicht gefunden
/home/$USER/testdaten/0/01/011/0072
0 1 1 0
mkdir: das Verzeichnis »/home/$USER/testdaten/0/01/011/0073“ kann nicht angelegt werden: Datei oder Verzeichnis nicht gefunden
/home/$USER/testdaten/0/01/011/0073
0 1 1 1
/home/$USER/testdaten/1
1 1 1 1
/home/$USER/testdaten/1/10
1 0 1 1
/home/$USER/testdaten/1/10/100
1 0 0 1
/home/$USER/testdaten/1/10/100/1000
1 0 0 0
/home/$USER/testdaten/1/10/100/1001
1 0 0 1

The error says cannot create the directory: file or directory not found

Answer 1

Just to elaborate a little, as this has already been solved...

printf "%04d\n" 0101 # leading zero tells %d this input is octal 65
0065

printf "%04s\n" 0101 # %s reads a string (but can still pad with 0's
0101