4.3(BOOL LOGIC) Flashcards
AND symbols
A ∧ B
A . B
AND circuit diagram
D (2 inputs 1 output)
OR symbols
A∨B
A+B
OR Circuit diagram
Star trek syymbol
2 inputs 1 output
Not symbols
¬A
_
A (bar A)
Not circuit diagram
Triangle followed by small circle
(no line in between)
XOR symbols
A(circled plus)B
A ∨ B
XOR rules (when does it output true and false)
Outputs TRUE if the inputs are different
Outputs FALSE if they are the same
XOR circuit
Curved line followed by star trek symbol
input lines go through the not line:
:):D-
A AND 0 =?
0
A AND 1=?
A
NOT A AND A= ?
0
A OR 0 = ?
A
A OR 1 = ?
1
NOT A OR A = ?
1
What is DeMorgans Law?
This provides a strategy for simplifying expressions that include a negation of a conjunction or disjunction (simplifying by inverting all variable)
(break the bar: change the sign)
NOT(A AND B) is the same as (NOT A) OR (NOT B)
Steps to DeMorgans Law?
Step 1
Change AND to OR (or vice versa) - ¬(A V B)
Step 2
NOT the terms either side of the operator - ¬(¬A V ¬B)
Step 3
NOT everything that has changed - ¬¬(¬A V ¬B)
Step 4
Get rid of any double negation - (¬A V ¬B)
Step 5
Remove any unnecessary brackets - ¬A V ¬B
Distributive law:
A.(B+C)=?
A+(B.C)=?
(A.B) + (A.C)
(A+B) . (A+C)
Negation law: ¬¬A=?
A
Q = ¬(A XOR B )=?
¬A . ¬B + A.B
A . ( (¬A . B) + (B . C ) )=?
(A . ¬A . B) + (A . B . C)
(0 . B) + (A . B . C)
0 + (A . B . C)
A . B . C
A + ( ¬A .B)=?
A + B
A . (¬A + B) = ?
A . B
Should you mix different expressions for Bool Logic?
NO
set 1:
A ^ B and
A V B or
¬A not
set 2:
A.B and
A+B or
_
A not
Inputs and outputs of a D-Type Flip Flop
Inputs:
- Data (D)
- Clock (CLK)
Outputs:
- Q
- ¬Q
Behaviour of D type (rising edge) Flip Flop
On the rising edge of the clock pulse:
If D is high (1), Q goes high and NOT(Q) goes low
If D is low (0), Q goes low and NOT(Q) goes high
The state of Q holds or “remembers” its value until the next rising clock edge
