Flip-flops Chapter4 Sequential circuits
Flip-flops Chapter4 Sequential circuits
sequential- Circuit Models Combinational logic X Universal combinational circuit model ■ No memory units No feedback from logic outputs back to the inputs
Combinational logic X0 Xn Y0 Ym Universal combinational circuit model ◼ No memory units ◼ No feedback from logic outputs back to the inputs
equential- CirCuit Model System Input System Variables工, output Combinational「 Variables logic State Variables xcitation 0 0 EV ariables Universa sequential circuit model
Combinational logic System Input Variables System output Variables I0 In O0 Om S0 Sx M0 Ex State Variables Excitation Variables MX E0 Universal sequential circuit model
equential Circuit Model a Sequential implies that events are ordered in time that one event then another occurs separated by time Two types of sequential logic exist: D Synchronous sequential circuit a Synchronous sequential circuit is clocked O Asynchronous sequential circuit a Asynchronous sequential circuit is not clocked
◼ Sequential implies that events are ordered in time, that one event then another occurs, separated by time. ◼ Two types of sequential logic exist: Synchronous sequential circuit ◼ Synchronous sequential circuit is clocked Asynchronous sequential circuit ◼ Asynchronous sequential circuit is not clocked
sequential- Circuit Model System Input System Variables工n output ombinational Variables logic ■SetI{工o…n} SetO{O0…On} are external are external input variables output variables presented to Excitation M the system Variables E
Combinational logic System Input Variables System output Variables I0 In O0 Om S0 Sx M0 Ex State Variables Excitation Variables MX E0 ◼ Set I{ I0……In } are external input variables presented to the system. ◼ Set O{ O0……Om } are external output variables
sequential- Circuit Models System Internally, the system generate the excitation variables, Eo to Ex, and state variables, So to Sx State Excitation Variables Variables ■ internal output M variables 0 a internal input variables X X
Combinational logic System Input Variables System output Variables I0 In O0 Om S0 Sx M0 Ex State Variables Excitation Variables MX E0 ◼ Internally, the system generate the excitation variables,E0 to Ex , and state variables, S0 to Sx . ◼ internal output variables ◼ internal input variables
sequential- Circuit Model Excitation variables Input Output (E Combinational Memory Combinational (O) transform (S) logic CLK M (9) State variables a The memory excitation input relationship can be written as D E=f(I, S) Excitation E force the memory elements to the desired state variables Output O is generated by the combinational logic transform, g), operating on input variables I and state variables s 口O=g(I,5)
◼ The memory excitation input relationship can be written as E = f( I, S ). Excitation E force the memory elements to the desired state variables. ◼ Output O is generated by the combinational logic transform, (g), operating on input variables I and state variables S. O = g( I, S ) Combinational transform (f) Memory M Combinational logic (g) Input (I) (E) CLK State variables (S) Excitation variables Output (O)
sequential- Circuit Model Excitation variables Input Output (E Combinational Memory Combinational (O) transform (S) logic CLK M (9) State variables ■E=f(工,S) ■O=g(工,5) a The clock input is not a binary value representing the time of day but rather a"synchronous"train of pulses. Synchronous memory changes its data only at certain time intervals
◼ E = f( I, S ) ◼ O = g( I, S ) ◼ The clock input is not a binary value representing the time of day, but rather a ”synchronous” train of pulses. Synchronous memory changes its data only at certain time intervals. Combinational transform (f) Memory M Combinational logic (g) Input (I) (E) CLK State variables (S) Excitation variables Output (O)
egwentislcirGuit Models ● State variab|es
•State variables
equential Circuit Model a State variable is the output of memory unit It is used to define the state of a sequential machine a State is defined by the content of memory Each state represent a different events. a State variables and states are related by 口2x y Dx= number of state variables Dy= number of States
◼ State variable is the output of memory unit. It is used to define the state of a sequential machine. ◼ State is defined by the content of memory. Each state represent a different events. ◼ State variables and states are related by 2x=y x= number of State variables y= number of States
