/\d1{1}/ matches any single decimal digit, "1" included, FOLLOWED BY a single "1".

toolic's YAPE explanation makes that clear, but your original spec indicates you want a single digit (known in advance, I gather).

Hence, /1{1}/ for a single "1" anywhere in a line, or /^1{1}$ for a line with a single "1" as its only content.