XOR | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
1 | 1 | 0 | 3 | 2 | 5 | 4 | 7 | 6 | 9 | 8 | B | A | D | C | F | E |
2 | 2 | 3 | 0 | 1 | 6 | 7 | 4 | 5 | A | B | 8 | 9 | E | F | C | D |
3 | 3 | 2 | 1 | 0 | 7 | 6 | 5 | 4 | B | A | 9 | 8 | F | E | D | C |
4 | 4 | 5 | 6 | 7 | 0 | 1 | 2 | 3 | C | D | E | F | 8 | 9 | A | B |
5 | 5 | 4 | 7 | 6 | 1 | 0 | 3 | 2 | D | C | F | E | 9 | 8 | B | A |
6 | 6 | 7 | 4 | 5 | 2 | 3 | 0 | 1 | E | F | C | D | A | B | 8 | 9 |
7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | F | E | D | C | B | A | 9 | 8 |
8 | 8 | 9 | A | B | C | D | E | F | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
9 | 9 | 8 | B | A | D | C | F | E | 1 | 0 | 3 | 2 | 5 | 4 | 7 | 6 |
A | A | B | 8 | 9 | E | F | C | D | 2 | 3 | 0 | 1 | 6 | 7 | 4 | 5 |
B | B | A | 9 | 8 | F | E | D | C | 3 | 2 | 1 | 0 | 7 | 6 | 5 | 4 |
C | C | D | E | F | 8 | 9 | A | B | 4 | 5 | 6 | 7 | 0 | 1 | 2 | 3 |
D | D | C | F | E | 9 | 8 | B | A | 5 | 4 | 7 | 6 | 1 | 0 | 3 | 2 |
E | E | F | C | D | A | B | 8 | 9 | 6 | 7 | 4 | 5 | 2 | 3 | 0 | 1 |
F | F | E | D | C | B | A | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Identities: x ⊕ 0 = x (i.e., 0 ⊕ 0 = 0, 1 ⊕ 0 = 1) x ⊕ 1 = ¬x (i.e., 0 ⊕ 1 = 1, 1 ⊕ 1 = 0) x ⊕ x = 0 (i.e., 0 ⊕ 0 = 0, 1 ⊕ 1 = 0) x ⊕ ¬x = 1 (i.e., 0 ⊕ 1 = 1) |
AND | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 |
3 | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 |
4 | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 |
5 | 0 | 1 | 0 | 1 | 4 | 5 | 4 | 5 | 0 | 1 | 0 | 1 | 4 | 5 | 4 | 5 |
6 | 0 | 0 | 2 | 2 | 4 | 4 | 6 | 6 | 0 | 0 | 2 | 2 | 4 | 4 | 6 | 6 |
7 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
9 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 8 | 9 | 8 | 9 | 8 | 9 | 8 | 9 |
A | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 8 | 8 | A | A | 8 | 8 | A | A |
B | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 | 8 | 9 | A | B | 8 | 9 | A | B |
C | 0 | 0 | 0 | 0 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | C | C | C | C |
D | 0 | 1 | 0 | 1 | 4 | 5 | 4 | 5 | 8 | 9 | 8 | 9 | C | D | C | D |
E | 0 | 0 | 2 | 2 | 4 | 4 | 6 | 6 | 8 | 8 | A | A | C | C | E | E |
F | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
Identities: x • 0 = 0 (i.e., 0 • 0 = 0, 1 • 0 = 0) x • 1 = x (i.e., 0 • 1 = 0, 1 • 1 = 1) x • x = x (i.e., 0 • 0 = 0, 1 • 1 = 1) x • ¬x = 0 (i.e., 0 • 1 = 0) |
OR | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
1 | 1 | 1 | 3 | 3 | 5 | 5 | 7 | 7 | 9 | 9 | B | B | D | D | F | F |
2 | 2 | 3 | 2 | 3 | 6 | 7 | 6 | 7 | A | B | A | B | E | F | E | F |
3 | 3 | 3 | 3 | 3 | 7 | 7 | 7 | 7 | B | B | B | B | F | F | F | F |
4 | 4 | 5 | 6 | 7 | 4 | 5 | 6 | 7 | C | D | E | F | C | D | E | F |
5 | 5 | 5 | 7 | 7 | 5 | 5 | 7 | 7 | D | D | F | F | D | D | F | F |
6 | 6 | 7 | 6 | 7 | 6 | 7 | 6 | 7 | E | F | E | F | E | F | E | F |
7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | F | F | F | F | F | F | F | F |
8 | 8 | 9 | A | B | C | D | E | F | 8 | 9 | A | B | C | D | E | F |
9 | 9 | 9 | B | B | D | D | F | F | 9 | 9 | B | B | D | D | F | F |
A | A | B | A | B | E | F | E | F | A | B | A | B | E | F | E | F |
B | B | B | B | B | F | F | F | F | B | B | B | B | F | F | F | F |
C | C | D | E | F | C | D | E | F | C | D | E | F | C | D | E | F |
D | D | D | F | F | D | D | F | F | D | D | F | F | D | D | F | F |
E | E | F | E | F | E | F | E | F | E | F | E | F | E | F | E | F |
F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | F |
Identities: x + 0 = x (i.e., 0 + 0 = 0, 1 + 0 = 1) x + 1 = 1 (i.e., 0 + 1 = 1, 1 + 1 = 1) x + x = x (i.e., 0 + 0 = 0, 1 + 1 = 1) x + ¬x = 1 (i.e., 0 + 1 = 1) |
XOR | AND | OR | |
---|---|---|---|
x ? 0 | x ⊕ 0 = x | x • 0 = 0 | x + 0 = x |
x ? 1 | x ⊕ 1 = ¬x | x • 1 = x | x + 1 = 1 |
x ? x | x ⊕ x = 0 | x • x = x | x + x = x |
x ? ¬x | x ⊕ ¬x = 1 | x • ¬x = 0 | x + ¬x = 1 |