This is a priority encoder. When the individual input lines are driven low, this chip outputs the index number of the highest-numbered input line that is low, in binary-encoded form, on its four output lines.
If inputs 2 and 6 are both low, the output is 6 (1010). If 6 and 8 are both low, the output is 8. If 2, 6, and 8 are low, the output is 8. And so on.