Boolean Logic

Logic Gates + Boolean Algebra + Algebraic Expressions + Adders + D-Type Flip Flops + Simplifying Boolean Expressions + De Morgan's Law

Define Boolean Algebra

Logical calculus of truth tables

• developed by George Boole (late 1830s)

• resembles algebra of real numbers but with numeric operations of: multiplication, addition and negation

• variables cam either be TRUE or FALSE (1s & 0s / 5v & 0v)

what is a logic gate

circuits which take boolean inputs and convert them to boolean output

• and

• or

• not

• nand

• nor

• xor

• xnor

Define Boolean Algebra

Logical calculus of truth tables

• developed by George Boole (late 1830s)

• resembles algebra of real numbers but with numeric operations of: multiplication, addition and negation

• variables cam either be TRUE or FALSE (1s & 0s / 5v & 0v)

what is a logic gate

circuits which take boolean inputs and convert them to boolean output

• and

• or

• not

• nand

• nor

• xor

• xnor

drawing truth tables: TRICK

n inputs = 2ⁿ lines in truth table

e.g. 3 inputs = 2³ = 8 lines in truth table

Draw the symbol, algebraic representation and truth table for the AND gate:

• A.B

• 0.0 = 0

• 0.1 = 0

• 1.0 = 0

• 1.1 = 1

Draw the symbol, algebraic representation and truth table for the OR gate:

• A+B

• 0+0 = 0

• 0+1 = 1

• 1+0 = 1

• 1 +1 = 1

Draw the symbol, algebraic representation and truth table for the NOT gate:

• A with a dash on top

• NOT 0 = 1

• NOT 1 = 0

draw the symbol, algebraic representation and truth table for NAND, NOR, XOR, XNOR gates: