OR GATE

At the bit level, there are four possibilities,
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1

XOR GATE

At the bit level, there are four possibilities,
0 ⊕ 0 = 0
0 ⊕ 1 = 1
1 ⊕ 0 = 1
1 ⊕ 1 = 0

NAND GATE

At the bit level, there are four possibilities,
0 ↑ 0 = 1
0 ↑ 1 = 1
1 ↑ 0 = 1
1 ↑ 1 = 0

AND GATE

At the bit level, there are four possibilities,
0 . 0 = 0
0 . 1 = 0
1 . 0 = 0
1 . 1 = 1

NOR GATE

At the bit level, there are four possibilities,
0 ↓ 0 = 1
0 ↓ 1 = 0
1 ↓ 0 = 0
1 ↓ 1 = 0

NOT GATE

At the bit level, there are four possibilities,
¬0 = 1
¬1 = 0