Without logging

output = 0

rednet.open('left')

while true do
  -- get our message
  local sender, msg, dist = rednet.receive()
  if sender == 45 and #msg == 2 then

    -- get the first part of our message and convert it from hex (base16) to decimal (base10)
    local num = tonumber(msg:sub(1,1), 16)

    -- if it was not hexadecimal
    if num then
      -- decide which function we should use based on if the second character is a t (for true)
      action = (msg:sub(2,2) == 't') and colors.combine or colors.subtract

      -- call out action with the current output and the one we just got
      output = action(output, 2 ^ num)

      -- everything is valid now lets output
      rs.setBundledOutput('back', output)
    end
  end
end

rednet.close('left')f