outline

Boolean logic

• Deals with manipulating the logical values true and false
• True would be represented by the binary value 1
• False would be represented by the binary value 0

Boolean Identities

• Or gate

  • Several ways to write ‘or’
    - OR ex: a OR b
    - ‘+’ ex: a + b
    - ‘v’ ex: a v b
    - or gate

  OR truth table

  • Lets build a truth table for A or B

  The OR gate

  • The logical operation of an OR gate is:
    
    

  Identity	Name
  x + x = x x * x = x	Idempotent laws
  x + 0 = x x * 1 = x	Identity laws
  x + 1 = 1 x * 0 = 0	Dominance laws
  x + y = y + x xy = yx	Commutative laws
  (x + y) + z = x + (y + z) x(yz) = (xy)z	Associative laws
  x + yz = (x + y )(x + z) x(y + z) = xy + xz	Distributive laws

  A	B	A OR B
  false	false	false
  true	false	true
  false	true	true
  true	true	true

Not gate

• Ways to write ‘not’
  - NOT ex: NOT a
  - ‘¬’ ex: a ¬ b
  - not gate

NOT truth table

• Let's build the NOT truth table

The NOT gate

• The logical operation of a NOT gate is:
  

  A	¬A
  false	True
  True	False

And gate

• Several ways to write ‘and’
  - AND ex: a AND b
  - ‘*’ ex: a * b
  - ‘^’ ex: a ^ b
  - ab
  - and gate

AND truth table

• Let's build the AND truth table

The AND gate

• The logical operation of an AND gate is:
  

  A	B	A ^ B
  false	false	false
  false	true	false
  true	false	false
  true	true	true

Virtual Logic Gate