1. Latch, Edge-Triggered Flip Flops

Latch is a bit storage device that do not need a clock pulse to enter the data. Edge-Triggered flip flop need a positive-edge or negative-edge, dependend on type, to enter the data. Most clocked flip flops also provide either or both or none at all of the RESET and PRESET inputs. Chapter 11 discuss latches created out of NAND or NOR gates. Popular clocked flip flops are: SR, JK, D and T.

2. Flip Flops, Truth Tables & Characteristic Equations

SR Truth Table & Characteristic Equation

	                        \ Qn
	S   R   Qn+1          SR \ 0   1
	------------          ----------
	0   0   Qn            00 | 0   1
	0   1   0             01 | 0   0     Qn+1 = S + R'Qn
	1   1   X             11 | X   X    
	1   0   1             10 | 1   1
	------------          ----------


	                        \ Qn
	J   K   Qn+1          JK \ 0   1
	------------          ----------
	0   0   Qn            00 | 0   1
	0   1   0             01 | 0   0     Qn+1 = JQn' + K'Qn
	1   1   Qn'           11 | 1   0  
	1   0   1             10 | 1   1
	------------          ----------


	                        Qn
	D   Qn+1              D \  0   1
	--------              ----------
	0   0                 0 |  0   0     Qn+1 = D
	1   1                 1 |  1   1
	--------              ----------


	                        Qn
	T   Qn+1              T \  0   1
	--------              ----------
	0   Qn                0 |  0   1     Qn+1 = T (+) Qn
	1   Qn'               1 |  1   0
	--------              ----------

3. Analysis & Design Samples using Method from Textbook

SAMPLE: Analyze the circuit by creating its "State Table"; draw the "Timing Diagram"

	PS         INPUTS     NS
	Q0 Q1 Q2   D0 D1 D2   Q0 Q1 Q2
	------------------------------
(MR)'->	0  0  0    0  0  1    0  0  1 
	0  0  1    1  0  1    1  0  1
	1  0  1    1  1  1    1  1  1
	1  1  1    1  1  0    1  1  0
	1  1  0    0  1  0    0  1  0
	0  1  0    0  0  0    0  0  0
	-----------------------------


	clock ___|___|___|___|___|___|___
                       ___________          
	Q0 __________|           |_______
                           ___________
	Q1 ______________|           |___
                   ___________
	Q2 ______|           |___________

SAMPLE: Use D-flip flops and design a circuit to generate the waveforms given in "Analysis" sample above. Rename the signals as A, B and C.

	       BC
	     A \ 00 01 11 10       00 01 11 10       00 01 11 10
	         -----------       -----------       -----------
	     0  | 0  1  X  0      | 0  0  X  0      | 1  1  X  0
	     1  | X  1  1  0      | X  1  1  1      | X  1  0  0
	         -----------       -----------       -----------

	           D1 = C              D2 = A           D3 = B'

The same circuit as in the analysis.

SAMPLE: Repeat design problem above using JK-flip flops.

	        BC
	     A \ 00 01 11 10       00 01 11 10       00 01 11 10
	         -----------       -----------       -----------
	     0  | 0  1  X  0      | 0  0  X  X      | 1  X  X  0
	     1  | X  X  X  X      | X  1  X  X      | X  X  X  0
	         -----------       -----------       -----------
	           J1 = C            J2 = A            J3 = B'


	        BC
	     A \ 00 01 11 10       00 01 11 10       00 01 11 10
	         -----------       -----------       -----------
	     0  | X  X  X  X      | X  X  X  1      | X  0  X  X
	     1  | X  0  0  1      | X  X  0  0      | X  0  1  X
	         -----------       -----------       -----------
	           K1 = C'           K2 = A'           K3 = B

HOMEWORK: Draw the circuit and analyze it. You must get the same waveforms.

4. Universal Map Method

Below we introduce symbols for Universal Map, Flip Flops Input "Excitation" requirement for the indicated output transition & derivation of the Flip Flops input equations.

	Symbols Use for Map Entry:
	
	Events        Qn  Qn+1  Entry
	-----------------------------
	turn-on       0   1     I
	turn-off      1   0     @
	stay-on       1   1     1
	stay-off      0   0     0
	-----------------------------


	Flip Flops Transition, Map Entry & Input Excitation Requirement:

	Qn   Qn+1  Entry       S   R       J   K        D        T
	----------------------------------------------------------
	0    0     0           0   X       0   X        0        0
	0    1     I           1   0       1   X        1        1
	1    1     1           X   0       X   0        1        0
	1    0     @           0   1       X   1        0        1
	----------------------------------------------------------


	Reading Rules:

	Flip Flop  Input Eqs  Must Include  Don't Include  Don't Care
	-------------------------------------------------------------
	SR         S          I             @, 0           1, X
	           R          @             I, 1           0, X
	-------------------------------------------------------------
	JK         J          I             0              @, 1, X
	           K          @             1              I, 0, X	
	-------------------------------------------------------------
	D          D          I, 1          @, 0           X
	-------------------------------------------------------------
	T          T          I, @          1, 0           X
	-------------------------------------------------------------

It is advisable to compare "Universal Map" to "textbook" multiple map method. In the next section we illustrate the flexibility of this method.

SAMPLE:Let's redesign the 3 waveforms using Universal Map.

Timing Waveforms:

	     clock ___|___|___|___|___|___|___
	                   ___________
	     A     _______|           |________
	                       ___________
	     B     ___________|           |____
	              ____________
	     C    ___|            |____________

	
	     BC
	  A \ 00 01 11 10       00 01 11 10       00 01 11 10
	      -----------       -----------       -----------
	  0  | 0  I  X  0      | 0  0  X  @      | I  1  X  0
	  1  | X  1  1  @      | X  I  1  1      | X  1  @  0
	      -----------       -----------       -----------
	         A FF              B FF              C FF

  	  D-FF: 
	       D1 = C            D2 = A             D3 = B'

	  SR-FF:
	       S1 = C            S2 = A             S3 = B'
	       R1 = C'           R2 = A'            R3 = B

	  JK-FF:
	       J1 = C            J2 = A             J3 = B'
	       K1 = C'           K2 = A'            K3 = B

	  T-FF:
	       T1 = AC' + A'C    T2 = A'B + AB'     T3 = B'C' + BC

Observe, one-map per flip flop is enough to derive inputs of "any" other type of flip flops. That is we only need 3 K-maps here. Employing the textbook multiple-map method we need to draw, 6SR + 6JK + 3D + 3T = 18 separate K-maps in all in order to obtain inputs of all four types of flip flops. Not to mention entering actual inputs of each flip flops is "not an easy task". In Universal Map on the other hand, map entry is based purely on "how" the machine behave and not based on "what" should their inputs be. There is "no need" to refer to the flip flop excitation table or truth table which is "time consuming" and prone to "human errors".

Return to Digital syllabus