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Algebraic normal form/table
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0
{\displaystyle 0}
[
]
{\displaystyle {\Bigl [}~{\Bigr ]}}
{
}
{\displaystyle {\Bigl \{}~{\Bigl \}}}
{
}
{\displaystyle {\Bigl \{}~{\Bigl \}}}
empty sum 0
0
{\displaystyle 0}
1
{\displaystyle 1}
[
(
)
]
{\displaystyle {\Bigl [}\left(~\right){\Bigr ]}}
{
{
}
}
{\displaystyle {\Bigl \{}\{~\}{\Bigl \}}}
{
0
}
{\displaystyle {\Bigl \{}0{\Bigl \}}}
2
0
{\displaystyle 2^{0}}
1
{\displaystyle 1}
a
{\displaystyle a}
[
(
a
)
]
{\displaystyle {\Bigl [}\left(a\right){\Bigr ]}}
{
{
0
}
}
{\displaystyle {\Bigl \{}\{0\}{\Bigl \}}}
{
1
}
{\displaystyle {\Bigl \{}1{\Bigl \}}}
2
1
{\displaystyle 2^{1}}
2
{\displaystyle 2}
¬
a
{\displaystyle \neg a}
[
(
)
,
(
a
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(a\right){\Bigr ]}}
{
{
}
,
{
0
}
}
{\displaystyle {\Bigl \{}\{~\},\{0\}{\Bigl \}}}
{
0
,
1
}
{\displaystyle {\Bigl \{}0,1{\Bigl \}}}
2
0
+
2
1
{\displaystyle 2^{0}+2^{1}}
3
{\displaystyle 3}
b
{\displaystyle b}
[
(
b
)
]
{\displaystyle {\Bigl [}\left(b\right){\Bigr ]}}
{
{
1
}
}
{\displaystyle {\Bigl \{}\{1\}{\Bigl \}}}
{
2
}
{\displaystyle {\Bigl \{}2{\Bigl \}}}
2
2
{\displaystyle 2^{2}}
4
{\displaystyle 4}
¬
b
{\displaystyle \neg b}
[
(
)
,
(
b
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(b\right){\Bigr ]}}
{
{
}
,
{
1
}
}
{\displaystyle {\Bigl \{}\{~\},\{1\}{\Bigl \}}}
{
0
,
2
}
{\displaystyle {\Bigl \{}0,2{\Bigl \}}}
2
0
+
2
2
{\displaystyle 2^{0}+2^{2}}
5
{\displaystyle 5}
a
⊕
b
{\displaystyle a\oplus b}
[
(
a
)
,
(
b
)
]
{\displaystyle {\Bigl [}\left(a\right),\left(b\right){\Bigr ]}}
{
{
0
}
,
{
1
}
}
{\displaystyle {\Bigl \{}\{0\},\{1\}{\Bigl \}}}
{
1
,
2
}
{\displaystyle {\Bigl \{}1,2{\Bigl \}}}
2
1
+
2
2
{\displaystyle 2^{1}+2^{2}}
6
{\displaystyle 6}
a
↔
b
{\displaystyle a\leftrightarrow b}
[
(
)
,
(
a
)
,
(
b
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right){\Bigr ]}}
{
{
}
,
{
0
}
,
{
1
}
}
{\displaystyle {\Bigl \{}\{~\},\{0\},\{1\}{\Bigl \}}}
{
0
,
1
,
2
}
{\displaystyle {\Bigl \{}0,1,2{\Bigl \}}}
2
0
+
2
1
+
2
2
{\displaystyle 2^{0}+2^{1}+2^{2}}
7
{\displaystyle 7}
a
∧
b
{\displaystyle a\land b}
[
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(a,b\right){\Bigr ]}}
{
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{0,1\}{\Bigl \}}}
{
3
}
{\displaystyle {\Bigl \{}3{\Bigl \}}}
2
3
{\displaystyle 2^{3}}
8
{\displaystyle 8}
¬
a
∨
¬
b
{\displaystyle \neg a\lor \neg b}
[
(
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(a,b\right){\Bigr ]}}
{
{
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{~\},\{0,1\}{\Bigl \}}}
{
0
,
3
}
{\displaystyle {\Bigl \{}0,3{\Bigl \}}}
2
0
+
2
3
{\displaystyle 2^{0}+2^{3}}
9
{\displaystyle 9}
a
∧
¬
b
{\displaystyle a\land \neg b}
[
(
a
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(a\right),\left(a,b\right){\Bigr ]}}
{
{
0
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{0\},\{0,1\}{\Bigl \}}}
{
1
,
3
}
{\displaystyle {\Bigl \{}1,3{\Bigl \}}}
2
1
+
2
3
{\displaystyle 2^{1}+2^{3}}
10
{\displaystyle 10}
¬
a
∨
b
{\displaystyle \neg a\lor b}
[
(
)
,
(
a
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(a,b\right){\Bigr ]}}
{
{
}
,
{
0
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{~\},\{0\},\{0,1\}{\Bigl \}}}
{
0
,
1
,
3
}
{\displaystyle {\Bigl \{}0,1,3{\Bigl \}}}
2
0
+
2
1
+
2
3
{\displaystyle 2^{0}+2^{1}+2^{3}}
11
{\displaystyle 11}
¬
a
∧
b
{\displaystyle \neg a\land b}
[
(
b
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(b\right),\left(a,b\right){\Bigr ]}}
{
{
1
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{1\},\{0,1\}{\Bigl \}}}
{
2
,
3
}
{\displaystyle {\Bigl \{}2,3{\Bigl \}}}
2
2
+
2
3
{\displaystyle 2^{2}+2^{3}}
12
{\displaystyle 12}
a
∨
¬
b
{\displaystyle a\lor \neg b}
[
(
)
,
(
b
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(b\right),\left(a,b\right){\Bigr ]}}
{
{
}
,
{
1
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{~\},\{1\},\{0,1\}{\Bigl \}}}
{
0
,
2
,
3
}
{\displaystyle {\Bigl \{}0,2,3{\Bigl \}}}
2
0
+
2
2
+
2
3
{\displaystyle 2^{0}+2^{2}+2^{3}}
13
{\displaystyle 13}
a
∨
b
{\displaystyle a\lor b}
[
(
a
)
,
(
b
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(a\right),\left(b\right),\left(a,b\right){\Bigr ]}}
{
{
0
}
,
{
1
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{0\},\{1\},\{0,1\}{\Bigl \}}}
{
1
,
2
,
3
}
{\displaystyle {\Bigl \{}1,2,3{\Bigl \}}}
2
1
+
2
2
+
2
3
{\displaystyle 2^{1}+2^{2}+2^{3}}
14
{\displaystyle 14}
¬
a
∧
¬
b
{\displaystyle \neg a\land \neg b}
[
(
)
,
(
a
)
,
(
b
)
,
(
a
,
b
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right),\left(a,b\right){\Bigr ]}}
{
{
}
,
{
0
}
,
{
1
}
,
{
0
,
1
}
}
{\displaystyle {\Bigl \{}\{~\},\{0\},\{1\},\{0,1\}{\Bigl \}}}
{
0
,
1
,
2
,
3
}
{\displaystyle {\Bigl \{}0,1,2,3{\Bigl \}}}
2
0
+
2
1
+
2
2
+
2
3
{\displaystyle 2^{0}+2^{1}+2^{2}+2^{3}}
15
{\displaystyle 15}
(
¬
a
∨
¬
b
∨
¬
c
)
∧
(
a
∨
b
)
{\displaystyle \left(\neg a\lor \neg b\lor \neg c\right)\land \left(a\lor b\right)}
[
(
a
)
,
(
b
)
,
(
a
,
b
)
,
(
a
,
b
,
c
)
]
{\displaystyle {\Bigl [}\left(a\right),\left(b\right),\left(a,b\right),\left(a,b,c\right){\Bigr ]}}
{
{
0
}
,
{
1
}
,
{
0
,
1
}
,
{
0
,
1
,
2
}
}
{\displaystyle {\Bigl \{}\{0\},\{1\},\{0,1\},\{0,1,2\}{\Bigl \}}}
{
1
,
2
,
3
,
7
}
{\displaystyle {\Bigl \{}1,2,3,7{\Bigl \}}}
2
1
+
2
2
+
2
3
+
2
7
{\displaystyle 2^{1}+2^{2}+2^{3}+2^{7}}
142
{\displaystyle 142}
(
a
∧
b
∧
c
)
∨
(
¬
a
∧
¬
b
)
{\displaystyle \left(a\land b\land c\right)\lor \left(\neg a\land \neg b\right)}
[
(
)
,
(
a
)
,
(
b
)
,
(
a
,
b
)
,
(
a
,
b
,
c
)
]
{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right),\left(a,b\right),\left(a,b,c\right){\Bigr ]}}
{
{
}
,
{
0
}
,
{
1
}
,
{
0
,
1
}
,
{
0
,
1
,
2
}
}
{\displaystyle {\Bigl \{}\{~\},\{0\},\{1\},\{0,1\},\{0,1,2\}{\Bigl \}}}
{
0
,
1
,
2
,
3
,
7
}
{\displaystyle {\Bigl \{}0,1,2,3,7{\Bigl \}}}
2
0
+
2
1
+
2
2
+
2
3
+
2
7
{\displaystyle 2^{0}+2^{1}+2^{2}+2^{3}+2^{7}}
143
{\displaystyle 143}
![{\displaystyle {\Bigl [}~{\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a9f09f1b572ca0173f2d2123e72b102f8979f18)
![{\displaystyle {\Bigl [}\left(~\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc066d13c587d95ddbc545c4fea3f1e1051ba7cd)
![{\displaystyle {\Bigl [}\left(a\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1ef15b2d9927ecdd8f999928765ca271d5f17de6)
![{\displaystyle {\Bigl [}\left(~\right),\left(a\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bace9634349a553a8b9ea0bb3e40002733e7e09)
![{\displaystyle {\Bigl [}\left(b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/187150ac73f92c9df47c663ea5169d63c107a2da)
![{\displaystyle {\Bigl [}\left(~\right),\left(b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c95917dd7b3ee0df008d4a6ca5a535697f670c)
![{\displaystyle {\Bigl [}\left(a\right),\left(b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f716ab45582bbac6fd339dc411bfba9278195a2)
![{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/65dcbad88c75c691447d89aa4fba6d4b6ef4853e)
![{\displaystyle {\Bigl [}\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ebe681ed4b35b3b61f02e20c826f5f70fe7413d)
![{\displaystyle {\Bigl [}\left(~\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9d8467c787a55c80aa1d6059ecea5df2ba20d76)
![{\displaystyle {\Bigl [}\left(a\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93d078cb073124902220b33be81e3b07149cf29f)
![{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6856cc5257710b6b8fa8116c945bab34a05bbda1)
![{\displaystyle {\Bigl [}\left(b\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbeb18f324a3a60a212c03114b1c4f2dfc41e82d)
![{\displaystyle {\Bigl [}\left(~\right),\left(b\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e6a34e5a7f66a17337652eb0fc1286f76232c0)
![{\displaystyle {\Bigl [}\left(a\right),\left(b\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af16546ba8e5496e3ad7e18d2778d54d1553d1d7)
![{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right),\left(a,b\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4097beda1a8882cf2c09be091196d2c2f19b086)
![{\displaystyle {\Bigl [}\left(a\right),\left(b\right),\left(a,b\right),\left(a,b,c\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/702b2c79d4dc135a139ffd4832510b9e2b8ecbd8)
![{\displaystyle {\Bigl [}\left(~\right),\left(a\right),\left(b\right),\left(a,b\right),\left(a,b,c\right){\Bigr ]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf094dc5f5f3e33d3a5ded3f319d1d72c5ea4db0)
