# Template:Algebraic normal form/table

 ${\displaystyle 0}$ ${\displaystyle {\Bigl [}~{\Bigr ]}}$ ${\displaystyle {\Bigl \{}~{\Bigl \}}}$ ${\displaystyle {\Bigl \{}~{\Bigl \}}}$ empty sum 0 ${\displaystyle 0}$ ${\displaystyle 1}$ ${\displaystyle {\Bigl [}\left(~\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0{\Bigl \}}}$ ${\displaystyle 2^{0}}$ ${\displaystyle 1}$ ${\displaystyle a}$ ${\displaystyle {\Bigl [}\left(a\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{0\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}1{\Bigl \}}}$ ${\displaystyle 2^{1}}$ ${\displaystyle 2}$ ${\displaystyle \neg a}$ ${\displaystyle {\Bigl [}\left(~\right),\left(a\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{0\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,1{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{1}}$ ${\displaystyle 3}$ ${\displaystyle b}$ ${\displaystyle {\Bigl [}\left(b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}2{\Bigl \}}}$ ${\displaystyle 2^{2}}$ ${\displaystyle 4}$ ${\displaystyle \neg b}$ ${\displaystyle {\Bigl [}\left(~\right),\left(b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,2{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{2}}$ ${\displaystyle 5}$ ${\displaystyle a\oplus b}$ ${\displaystyle {\Bigl [}\left(a\right),\left(b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{0\},\{1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}1,2{\Bigl \}}}$ ${\displaystyle 2^{1}+2^{2}}$ ${\displaystyle 6}$ ${\displaystyle a\leftrightarrow b}$ ${\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{0\},\{1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,1,2{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{1}+2^{2}}$ ${\displaystyle 7}$ ${\displaystyle a\land b}$ ${\displaystyle {\Bigl [}\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}3{\Bigl \}}}$ ${\displaystyle 2^{3}}$ ${\displaystyle 8}$ ${\displaystyle \neg a\lor \neg b}$ ${\displaystyle {\Bigl [}\left(~\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,3{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{3}}$ ${\displaystyle 9}$ ${\displaystyle a\land \neg b}$ ${\displaystyle {\Bigl [}\left(a\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{0\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}1,3{\Bigl \}}}$ ${\displaystyle 2^{1}+2^{3}}$ ${\displaystyle 10}$ ${\displaystyle \neg a\lor b}$ ${\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{0\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,1,3{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{1}+2^{3}}$ ${\displaystyle 11}$ ${\displaystyle \neg a\land b}$ ${\displaystyle {\Bigl [}\left(b\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{1\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}2,3{\Bigl \}}}$ ${\displaystyle 2^{2}+2^{3}}$ ${\displaystyle 12}$ ${\displaystyle a\lor \neg b}$ ${\displaystyle {\Bigl [}\left(~\right),\left(b\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{1\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,2,3{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{2}+2^{3}}$ ${\displaystyle 13}$ ${\displaystyle a\lor b}$ ${\displaystyle {\Bigl [}\left(a\right),\left(b\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{0\},\{1\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}1,2,3{\Bigl \}}}$ ${\displaystyle 2^{1}+2^{2}+2^{3}}$ ${\displaystyle 14}$ ${\displaystyle \neg a\land \neg b}$ ${\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right),\left(a,b\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{0\},\{1\},\{0,1\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,1,2,3{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{1}+2^{2}+2^{3}}$ ${\displaystyle 15}$ ${\displaystyle \left(\neg a\lor \neg b\lor \neg c\right)\land \left(a\lor b\right)}$ ${\displaystyle {\Bigl [}\left(a\right),\left(b\right),\left(a,b\right),\left(a,b,c\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{0\},\{1\},\{0,1\},\{0,1,2\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}1,2,3,7{\Bigl \}}}$ ${\displaystyle 2^{1}+2^{2}+2^{3}+2^{7}}$ ${\displaystyle 142}$ ${\displaystyle \left(a\land b\land c\right)\lor \left(\neg a\land \neg b\right)}$ ${\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right),\left(a,b\right),\left(a,b,c\right){\Bigr ]}}$ ${\displaystyle {\Bigl \{}\{~\},\{0\},\{1\},\{0,1\},\{0,1,2\}{\Bigl \}}}$ ${\displaystyle {\Bigl \{}0,1,2,3,7{\Bigl \}}}$ ${\displaystyle 2^{0}+2^{1}+2^{2}+2^{3}+2^{7}}$ ${\displaystyle 143}$