1.4.3

• Boolean logic


  Defines problems that can equate to either True or False, but not both
• Manipulating Boolean expressions


  Karnaugh maps to simplify Boolean expressions
• Rules to derive or simplify statements in Boolean algebra

  • De Morgan's Laws
  • Distribution
  • Association
  • Commutation
  • Double negation
• Logic gate diagrams and truth tables


  Used to represent Boolean logic
• Logic associated with D type flip flops, half and full adders


  • D type flip flops store the value of one bit
  • Half adders have two inputs (A and B) and two outputs (Sum and Carry)
  • Full adders have three inputs (A, B and Carry in) and two outputs (Sum and Carry out)
• Conjunction is applied to two literals (or inputs) to produce a single output
• Disjunction operates on two literals and produces a single output
• Negation is only applied to one literal and reverses the truth value of the input
• Exclusive disjunction (XOR) only outputs True when exactly one input is True
• Boolean equations are made by combining Boolean operators
• Karnaugh maps can be used to simplify Boolean expressions
• De Morgan's laws involve breaking a negation and changing the operator between two literals
• Distribution applies to conjunction over disjunction as well as disjunction of conjunction
• Associative laws involve the addition or removal of brackets and reordering of literals in a Boolean expression
• Laws of commutation show that the order of literals around an operator does not matter
• If you negate a literal twice, you can remove both negations and retain the same truth value
• A D-type flip flop uses four NAND gates and updates the value of Q to the value of D whenever the clock (CLK) ticks, on a rising edge
• A half adder has two inputs (A and B) and two outputs (Sum and Carry)
• A full adder has three inputs (A, B and Carry in) and two outputs (Sum and Carry out)
• Circuits of full adders can be chained together to form a ripple adder