1.4.3 Boolean Algebra

• What can problems be defined using in Boolean logic?

  Boolean equations
• What are the possible truth values of a Boolean equation?

  True or False
• What are the four operations in Boolean logic?

  • Conjunction
  • Disjunction
  • Negation
  • Exclusive Disjunction
• What is the symbol for conjunction in logic gates?

  AND
• What is the symbol for disjunction in logic gates?

  OR
• What is the symbol for negation in logic gates?

  NOT
• What is the symbol for exclusive disjunction in logic gates?

  XOR
• What does a truth table show?

  Every possible permutation of inputs
• How are inputs usually labeled in a truth table?


  A, B, C, etc.
• When is the output of an AND gate True?

  When both inputs are True
• What is the output of an AND gate when both inputs are False?

  False (0)
• How does conjunction (AND) operate on inputs?

  • Applies to two literals
  • Produces a single output
  • Can be thought of as multiplication
• How does disjunction (OR) operate on inputs?

  Produces True if at least one input is True
• What is the output of an OR gate when both inputs are False?

  False (0)
• How does negation (NOT) operate on an input?

  • Applied to one literal
  • Reverses the truth value
  • Example: NOT 1 is 0
• When does exclusive disjunction (XOR) output True?

  When exactly one input is True
• What is the output of an XOR gate when both inputs are True?

  False (0)
• What is the process for combining Boolean operations?

  • Combine Boolean operators like standard math
  • Create Boolean equations
  • Use truth tables for combinations
• What is a Karnaugh map used for?

  To simplify Boolean expressions
• What must the values in a Karnaugh map be written using?

  Gray code
• How do you highlight 1s in a Karnaugh map?

  Using rectangles of power of 2
• What does overlapping rectangles in a Karnaugh map allow?

  It is beneficial for simplification
• What are De Morgan's Laws in Boolean algebra?

  • Break a negation
  • Change the operator between literals
  • Negate both literals

  
• What is distribution in Boolean algebra?

  • Applies to conjunction over disjunction
  • Applies to disjunction of conjunction
  • Can be carried out over the same operator
• What do associative laws in Boolean algebra involve?

  • Addition or removal of brackets
  • Reordering of literals
• What do commutation laws in Boolean algebra show?

  • The order of literals does not matter
• What does double negation in Boolean algebra state?

  • Negating a literal twice retains the truth value
• What is a D-Type Flip Flop?

  • A logic circuit that stores one bit
  • Has two inputs: control signal and clock

  
• When does the output of a D-type flip flop change?

  At the rising edge of the clock
• What is the function of an adder in logic circuits?

  • Adds together true inputs
  • Outputs the sum in binary

  
• What are the two types of adders?

  • Half Adder
  • Full Adder
• How does a half adder operate?

  • Has two inputs: A and B
  • Outputs: Sum and Carry
  • Uses AND and XOR gates

  
• What is the truth table output for a half adder when both inputs are true?

  Sum is True, Carry is True
• How does a full adder differ from a half adder?

  • Has an additional input for carry
  • Outputs include Cout and Sum

  
• How many rows are in the truth table for a full adder?

  Eight rows
• What can be connected to a full adder's inputs?

  Previous adder's outputs and new input
• And (∧)

  Conjunction (Returns TRUE if both operands are TRUE)
• Or (∨)

  Disjunction (Returns TRUE if at least one operand is TRUE)
• Not (¬)

  Negation (Returns the opposite of the operand)
• XOR (⊕)

  Exclusive Disjunction (Returns TRUE if only one operand is TRUE, and FALSE if both or neither are TRUE)