circuits with flip-flop = sequential circuit circuit...
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Circuit, State Diagram, State Table, g ,
Circuits with Flip-Flop = Sequential Circuit
Circuit = State Diagram = State Table
State MinimizationState Minimization
Sequential Circuit Design
Example: Sequence Detector
Example: Binary Counterp y
Circuit, State Diagram, State Table
Terms:
Circuit, State Diagram, State Table
Terms:
State: flip-flop output combination
Present state: before clockNext state: after clock
State transition <= clock
1 flip-flop => 2 states2 flip-flops => 4 states3 flip flops => 8 states3 flip-flops => 8 states4 flip-flops => 16 states
... ...NN flip-flops => 2N states
Sequential circuit components:
Circuit, State Diagram, State Table
Sequential circuit components:
Flip-flop(s)ClockClockLogic gatesInputOutput
State diagram:
Circuit, State Diagram, State Table
State diagram:
Circle => state
Arrow => transitioninput/output
State table:
Circuit, State Diagram, State Table
State table:
Left column => current state
Top row => input combination
Table entry => next state, output
Example: Binary Counter
1110 1111 0000 0001... 1110 1111 0000 0001 0010 0011 0100 0101 ...ce
next statepresent state ce=0 ce=1
0000 0000 00010001 0001 00100010 0010 0011 state table16 ... ... ...1101 1101 11101110 1110 11111111 1111 0000
state table16states
1 1 1 1
0 0 0 0 0
1
1state diagram
1
...
11 1 1 1
0 0 0 0 0
Circuit, State Diagram, State Table
Example:Example:
Circuit, State Diagram, State Table
Example:Example:
Input and output valuesInput and output values separated by dash along the directed lines
Meal t peMealy-type
Circuit, State Diagram, State Table
Example:Example:
Circuit, State Diagram, State Table
Example:Example:
state diagram state tablestate table
Circuit, State Diagram, State Table
Example: Moore-typeExample: yp
• Input values labeled alongthe directed linesthe directed lines
• Output values indicatedinside the circles
Circuit, State Diagram, State Table
Example: Show the second form truth table similar to Table 5.3Example: Show the second form truth table similar to Table 5.3
00 01
0 0
1/0 /000 01
11
/0 /0
1011 1 /0/1
00
i itcircuit state table state diagramstate diagram
Circuit, State Diagram, State Table
Example: state diagram = state tableExample: state diagram state tablestate table/state diagram
circuit
D-FF characteristic eq: D = Q*
00 01 11 100 0 0 0 0
ABx
DA
00 01 11 100 0 0 0 0
ABx
DB
00 01 11 100 0 0 0 0
ABx
z1 0 1 1 1
A1 1 0 0 0
B1 0 0 1 1
DA=Ax+Bx DB=A’B’x z=Ax
z=Axx
SETDA=Ax+Bx
A
Q
QSET
CLR
D A
QSETDDB=A’B’x
B
QCLR
Circuit, State Diagram, State Table
Example: Show the state diagram of following circuitExample: Show the state diagram of following circuit
Circuit, State Diagram, State Table
Example: Show the state diagram of following circuitExample: Show the state diagram of following circuit
0
000 01/0 /0
0
0
1
00 1
1011 /0/1
11
y = ABD = Ax+BxDA = Ax+BxDB = Ax+B’x
Circuit, State Diagram, State Table
Example: Show the second form truth tableExample: Show the second form truth table
From circuit (equations)
y = ABDA = Ax+BxD = Ax+B’x
x: input, y: outputA, B: present stateD D : next state (D-FF)DB = Ax+B x DA, DB: next state (D-FF)
From state diagram
S0
S1
S2
S3
Circuit, State Diagram, State Table
More Example: Binary Counter – show state diagram and tableMore Example: Binary Counter show state diagram and table
Circuit, State Diagram, State Table
More Example: Binary Counter – show state diagram and tableMore Example: Binary Counter show state diagram and table
present state
next statestate
A2 A1 A0
state
0 0 00 0 1
A2 A1 A0
0 0 10 1 00 0 1
0 1 00 1 11 0 0
0 1 00 1 11 0 01 0 11 0 0
1 0 11 1 01 1 1
1 0 11 1 01 1 10 0 0
Circuit, State Diagram, State Table
More Example: Word ProblemMore Example: Word ProblemDesign a 2-bit complex counter with one input x that can be- a down counter when x=0 (... 11 10 01 00 11 ...)
J h t h 1 ( 00 01 11 10 00 )- a Johnson counter when x=1 (... 00 01 11 10 00 ...)
00 010
1 present state
next statex=0 x=1
00 1 1
stateA B
x 0 x 1A B A B
0 00 1
1 10 0
0 11 1
11 100
1
0 11 01 1
0 00 11 0
1 10 01 0
0
present state
next statex=0 x=1 AB
DAAB
DBstateA B
x 0 x 1A B A B
0 00 1
1 10 0
0 11 1
00 01 11 1001
x1 0 1 00 1 1 0
00 01 11 1001
x1 0 0 11 1 0 0
0 11 01 1
0 00 11 0
1 10 01 0
DA=AB+Bx+A’B’x’ DB=B’x’+A’x
x ADA
BDB
clock
Circuit, State Diagram, State Table
Quiz:Quiz:
http://www.eelab.usyd.edu.au/digital_tutorial/part3/t-diag.htm
Circuit, State Diagram, State Table
Quiz: solutionQuiz: solution
http://www.eelab.usyd.edu.au/digital_tutorial/part3/t-diag.htm
Circuit, State Diagram, State Table
More Example:More Example:
http://www.eelab.usyd.edu.au/digital_tutorial/part3/example1-1.htm