XOR TABLE (HEX)

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 TABLE (HEX)

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 TABLE (HEX)

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)




THE IDENTITIES SUMMARIZED

  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


GCK, 12/18/2000
(10/29/2012)