| 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) |
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| 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) |
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| 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) |
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| 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 |