It's easier with zsh:

for ((i=2#$a; i<=2#$b; i++)) echo $(([##2]i))

Otherwise you can use bc:

echo "ibase=obase=2; for (i=$a; i<=$b; i++) i" | bc

Or dc:

echo "2doi $a [p1+d$b!<a]dsax" | dc

It's easier with zsh:

for ((i=2#$a; i<=2#$b; i++)) echo $(([##2]i))

Or with 0-padding:

for ((i=2#$a; i<=2#$b; i++)) printf '%04d\n' $(([##2]i))

Otherwise you can use bc:

echo "ibase=obase=2; for (i=$a; i<=$b; i++) i" | bc

Or dc:

echo "2doi $a [p1+d$b!<a]dsax" | dc

To 0-pad, you can always pipe the output to:

sed 's/^/000/;s/^0*\(.\{4\}\)/\1/'

It's easier with zsh:

for ((i=2#0011; i<2#1000; i++)) echo $(([##2]i))

It's easier with zsh:

for ((i=2#$a; i<=2#$b; i++)) echo $(([##2]i))

Otherwise you can use bc:

echo "ibase=obase=2; for (i=$a; i<=$b; i++) i" | bc

Or dc:

echo "2doi $a [p1+d$b!<a]dsax" | dc