non negative integers one of which must be either 0 or 1 usually q a q a q b q b but this is not always so for addition there are the following five cases e a 0 e b gt 0 e c gt 0 q a q a u2212 1 q b q b 7 e a gt 0 e b 0 e c gt 0 q a q a q b q b u2212 1 8 e a 0 e b 0 e c gt 0 q a q a u2212 1 q b q b u2212 1 9 for subtraction the outcome is similar with c round a u2212 b there are q b e a u2212 e b q c e a u2212 e c q b e a u2212 e b and q c e a u2212 e c where one of q b q c is either 0 or 1 and one of q b q c is either 0 or 1 thus there are an additional five cases e c 0 e b gt 0 e a gt 0 q c q c u2212 1 q b q b 12 e c gt 0 e b 0 e a gt 0 q c q c q b u2212 q b u2212 1 13 e c 0 e b 0 e a gt 0 q c q c u2212 1 q b.