Lecture 5 Flashcards
Commutativity
Order of inputs for AND or OR function doesn’t affect value of output
(B and C) = (C and B)
Dual: B+C = C+B
Associativity
Specific groupings of inputs do not affect the value of the output
(B and C) and D = B and (C and D)
Dual: (B+C) + D = B + (C+D)
Distributivity
AND distributes over OR
(B and C) + (B and D) = B and (C+D)
Dual: OR distributes over AND
(B+C) and (B+D) = B+(C and D)
Covering, combining, and consensus
Allows us to eliminate redundant variables
Covering
B and (B+C) = B
Dual: B + (B and C) = B
Combining
(B and C) + (B and ~C) = B
Dual: (B+C) and (B+~C) = B
Consensus
(B and C) + (~B and D) + (C and D) = B and C + ~B and D
Dual: (B+C) and (~B+D) and (C+D) = (B+C) and (~B+D)
De Morgan’s Theorem
Complement of product of all terms equals sum of complements of each term
Dual: complement of sum of all terms equals product of complements of each term
NAND = OR with inverted inputs
NOR = AND with inverted inputs
Bubble
The inversion circuit on a logic gate
NAND gate: pushing bubbles from right to left
OR body with bubbles on inputs
Rules for bubble pushing
Pushing bubbles backward (from output) or forward (from input) changes the body of the gate from AND to OR or vice versa
Bubble pushing backward from output back to inputs puts bubbles on all gate inputs
Pushing bubbles forward from all gate inputs toward outputs puts a bubble on the output
Prime implication
If it cannot be combined with any other implicates to form a new implicant with fewer literals
Schematic
A diagram of a digital circuit showing the elements and wires that connect them together
Wires connect at a _
T junction
Connection between wires
Dot where wires cross
