1 / 9

Sequential Circuits

Sequential Circuits. Analysis. Inputs. Combina-tional Logic. Outputs. Storage Elements. Next State. State. CLK. Sequential Circuit Analysis. Current State at time (t) is stored in a n array of flip-flops . Next State at time (t+1) is a Boolean function of S tate and Inputs .

oona
Download Presentation

Sequential Circuits

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SequentialCircuits Analysis

  2. Inputs Combina-tional Logic Outputs Storage Elements Next State State CLK Sequential Circuit Analysis • Current Stateat time (t) is stored in an array of flip-flops. • Next State at time (t+1) is a Boolean function of State and Inputs. • Outputsat time (t) are a Boolean function of State (t) and (sometimes) Inputs (t).

  3. Example of a SequentialCircuit Input: x(t) Output:y(t) State:(A(t), B(t)) • What is theOutput Function? • What is the Next State Function? x A Q D A Q C Next State B Q D CP Q' C y Output

  4. Present State Input Next State Output Present Next State Output A(t) B(t) x(t) A(t+1) B(t+1) y(t) State x(t)=0 x(t)=1 x(t)=0 x(t)=1 0 0 0 0 0 0 A(t) B(t) A(t+1)B(t+1) A(t+1)B(t+1) y(t) y(t) 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 State Table A(t+1) = A(t)x(t)+B(t)x(t) B(t+1) =A (t)x(t) y(t) =x (t)(B(t)+A(t))

  5. x=0/y=0 x=0/y=1 x=1/y=0 A B 1 0 0 0 x=0/y=1 x=1/y=0 x=1/y=0 x=0/y=1 1 1 0 1 x=1/y=0 State Diagrams • The sequential circuit function can be represented in graphical form as a state diagram

  6. MEALY MACHINE MOORE MACHINE Inputs X(t) Outputs Z(t) Inputs X(t) Combinational circuits Combinational circuits Storage Element S(t) Storage Element S(t) Outputs Z(t) Moore and Mealy Models • Moore Model • Outputs are a function ONLY of states • Mealy Model • Outputs are a function of inputs AND states

  7. x=1/y=0 x=0/y=0 1 0 Present Next State Output x=0/y=0 State x=0 x=1 x=0 x=1 x=1/y=1 0 0 1 0 0 x=0 1 0 1 0 1 0/0 x=0 Present Next State Output x=1 State x=0 x=1 x=1 x=0 0 0 1 0 1 0 2 0 2/1 1/0 2 0 2 1 x=1 Moore and Mealy Example StateDiagrams Mealy Moore

  8. 0/0 1/0 S0 S1 0/1 0 1 1/0 0/1 S0/0 S1 0/1 S2 0/1 1/0 1/0 0/1 0/0 1/0 1/0 S0 S1 S3 S2 0/1 1/0 1/0 Equivalent States • Twostatesareequivalentif: • Outputproducedforeachinput is identical • Thenextstatesforeachinputaresameorequivalent

  9. A Z D Q Q C R B D Q Q C R C D Q Clock Q C R Reset SequentialAnalysisExample • Variables • Inputs: None • Outputs: Z • State Variables: A, B, C • FlipFlopInputEquations • A(t+1) = • B(t+1) = • C(t+1) = • Z = Mealy? Moore? StateTable? StateDiagram?

More Related