adder.sed

# invoke with, ex., 'echo "10010 10110" | sed -rf adder.sed'
:add
p
# If we have two final zeroes:
/^[01]*0\s[01]*0$/ {
  # drop the final zeroes
  s/^([01]*)0(\s)([01]*)0$/\1\2\3/
  # swap the hold buffer in
  x
  # add a 0 at the front
  s/^/0/
  p; x; /[01]+/ b add
}
# If we have one final one:
/^([01]*0\s[01]*1|[01]*1\s[01]*0)$/ {
  # drop the final digits
  s/^([01]*).(\s)([01]*).$/\1\2\3/
  # swap the hold buffer in
  x
  # add a 1 at the front
  s/^/1/
  p; x; /[01]+/ b add
}
# If we have two final ones:
/^[01]*1\s[01]*1$/ {
  # drop the final digits
  s/^([01]*)1(\s)([01]*)1$/\1\2\3/
  # swap the hold buffer in and add a C (for Carry)
  x
  s/^/C/
  p; x; /[01]+/ b add
}
/^\s*[01]+\s*$/ {
  # prepend the pattern buffer to the hold buffer
  x; H
  # remove the spaces
  x; s/\s*//g
  p; x; /[01]+/ b add
}
/[01]+/! x

:carry
s/(^|0)C/10/g
s/1C/C0/g
p
/C/ b carry