# Boolean Algebra

### AND Gate

x |
y |
F |

0 |
0 |
0 |

0 |
1 |
0 |

1 |
0 |
0 |

1 |
1 |
1 |

### OR Gate

- Nose cone shape, triangular

x |
y |
F |

0 |
0 |
0 |

0 |
1 |
1 |

1 |
0 |
1 |

1 |
1 |
1 |

### NOT Gate

- Also known as inverter
- Symbol is triangle with dot on top

### Operators

- Basic operators (more later)
- AND = multiplication
- OR = addition
- NOT = ‘ or top-bar

Ex.

- F(a,b,c) = ab+c+ac’
- What are the variables?
- What are the literals?
- What are the product terms?

### Commutativity

- Communtative
- a + b = b + a
- ab = ba

### Distributive

- a(b + c) = ab + ac
- a + (bc) = (a + b)(a + c)

### Associative

### Identity

- a + 0 = 0 + a = a
- a1 = 1a = a

### Complementary

### Null

### Idempotent Law

### DeMorgan’s Law

- (a + b)’ = a’b’
- (ab)’ = a’ + b’

### Absoption Law

### Theorem

- a + a’b = a + b
- a(a’ + b) = ab

Ex.

- F = x’yz + x’yz’ + xz
- Simplify
- F = x’y(z + z’) + xz
- F = x’y + xz