bubble correction
It is true that if a bubble occurs near the top thermometer code, gray output remains fairly close to the top of thermometer code. But if a bubble occurs far from the top, ex at the eight's bit, the gray code will be 0011, quite away from 1011. So how does gray correct such bubble?
thermometer code gray code equivalent devimal output
no bubble: 111111111111100 1011 13
one bubble: 111111111111010 1000 15
two bubble: 111111111111001 1010 12
one bubble: 111111101111100 0011 3