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CENG 241 Digital Design 1 Lecture 9. Amirali Baniasadi amirali@ece.uvic.ca. This Lecture. Review of last lecture JK, T Flip-Flops Direct Inputs, Analysis of Clocked Sequential Circuits. Graphic Symbols. Other Flip-Flops. Each flip-flop is made of interconnection of gates.

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ceng 241 digital design 1 lecture 9

CENG 241Digital Design 1Lecture 9

Amirali Baniasadi

amirali@ece.uvic.ca

this lecture
This Lecture
  • Review of last lecture
  • JK, T Flip-Flops
  • Direct Inputs, Analysis of Clocked Sequential Circuits
other flip flops
Other Flip-Flops
  • Each flip-flop is made of interconnection of gates.
  • The edge-triggered D flip-flop is the most efficient flip-flop since it requires the least number of gates.
  • Other flip-flops are made using the D flip-flop and extra logic.
  • Two flip-flops widely used are the JK andTflip-flop.
jk flip flop
JK Flip-Flop
  • Three flip-flop operations: Set, Reset, Complement output.
  • JK performs all three
slide6

JK Flip-Flop

D = JQ’ + K’Q

if J=1 , K=0 then D=Q’+Q=1

if J=0 , K=1 then D=0

if j =1 , K=1 then D = Q’

slide7

T Flip-Flop

T (Toggle) flip-flop is a complementing one.

T flip-flop is obtained from a JK when inputs J and K are tied together.

slide8

T Flip-Flop

If T=0 ( J=K=0) output does not change.

If T=1 ( J=K=1) output is complemented.

A T flip-flop can also be made of D flip-flop and a XOR.

D = T XOR Q = TQ’ + T’Q

characteristic tables
Characteristic Tables
  • JK Flip-flop
  • J K Q(t+1)
  • 0 0 Q(t) No change
  • 0 1 0 Reset
  • 1 0 1 Set
  • 1 1 Q’(t) Complement
characteristic tables1
Characteristic Tables
  • D Flip-flop
  • D Q(t+1)
  • 0 0 Reset
  • 1 1 Set
  • T Flip-flop
  • T Q(t+1)
  • 0 Q(t) No change
  • 1 Q’(t) Complement
slide11

Direct Inputs

Some flip-flops have asynchronous inputs to force the flip-flop to a particular state.

Examples: Direct Set, Direct Reset.

The input that sets the flip-flop to 1 is called preset or direct set.

The input that clears the flip-flop to 0 is called clear or direct reset.

Works independent of clock.

slide12

Direct Inputs: Asynchronous Reset

When reset is 0, Q’ is forced to 1.

analysis of clocked sequential circuits
Analysis of Clocked Sequential Circuits
  • Analysis: Obtaining a table/diagram for the time sequence of inputs/outputs/internal states.
  • Examples: State Equations, State Table, State Diagram
slide14

Analysis of Clocked Sequential Circuits

Example of state equation:

A(t+1) = A(t)x(t) + B(t)x(t)

B(t+1) = A’(t)x(t)

A(t+1)=Ax+Bx

B(t+1)=A’x

y(t)=(A(t)+B(t)).x’(t)

= (A+B)x’

example of state tables
Example of state tables
  • Present state input Next State Output
  • A B x A B y
  • 0 0 0 0 0 0
  • 0 0 1 0 1 0
  • 0 1 0 0 0 1
  • 0 1 1 1 1 0
  • 1 0 0 0 0 1
  • 1 0 1 1 0 0
  • 1 1 0 0 0 1
  • 1 1 1 1 0 0

State equation:

A(t+1) = A(t)x(t) + B(t)x(t)

B(t+1) = A’(t)x(t)

y(t)=(A(t)+B(t)).x’(t)

example of state tables 2nd form
Example of state tables-2nd form
  • Present state Next State Output
  • x=0 x=1 x=0 x=1
  • AB AB AB y y
  • 00 00 01 0 0
  • 01 00 11 1 0
  • 10 00 10 1 0
  • 11 00 10 1 0

State equation:

A(t+1) = A(t)x(t) + B(t)x(t)

B(t+1) = A’(t)x(t)

y(t)=(A(t)+B(t)).x’(t)

slide17

Example of state diagram

Present state Next State Output

x=0 x=1 x=0 x=1

AB AB AB y y

00 00 01 0 0

01 00 11 1 0

10 00 10 1 0

11 00 10 1 0

slide19

Analysis: JK flip-flop

JA=B

KA=Bx’

J B=x’

KB=A’x+Ax’

slide20

Analysis: JK flip-flop

A(t+1)=JA’+K’A

B(t+1)=JB’+K’B

A(t+1)=BA’+(Bx’)’A=A’B+AB’+Ax

B(t+1)=x’B’+(A XOR x’)B

=B’x’+ABx+A’Bx’

slide21

Analysis: JK flip-flop

Present state input Next State

A B x A B

0 0 0 0 1

0 0 1 0 0

0 1 0 1 1

0 1 1 1 0

1 0 0 1 1

1 0 1 1 0

1 1 0 0 0

1 1 1 1 1

slide22

Analysis: T flip-flop

Q(t+1)=T’Q+TQ’

TA=Bx

TB=x

y=AB

A(t+1)=(Bx)’A+(Bx)A’

=AB’+Ax’+A’Bx

B(t+1)=x XOR B

summary
Summary
  • Analysis
  • Reading up to page 214