# CS 6020 - Chapter 3 (3A and 10.2.2) CS 6020 - Chapter 3 (3A and 10.2.2) Part 5 of 5 Dr. Clincy Professor of CS Maybe some time will be remaining after tonights class for final project teams to meet Dr. Clincy Lecture Slide 1 Sequential Circuits Vs Combinational Circuits New Input Current State or Output Current State or output of the device is affected by the previous states Flip Flops Previous State or Output Circuit Sequential Logic Previous State or Output New Input Dr. Clincy

Circuit Combinatorial or Combinational Logic Current State or Output Current State or output of the device is only affected by the current inputs Lecture 2 Clock - Sequential Circuits State changes are controlled by clocks (clock ticks). Circuits can change state on the rising edge, falling edge, or when the clock pulse reaches its highest voltage edge triggered. Level-triggered circuits change state when the clock voltage reaches its highest or lowest level. Dr. Clincy Lecture 3 Current State or Output S and R stand for set and reset respectively constructed from a pair of cross-coupled NOR gates the stored bit is present on the output marked Qa If S and R inputs are both low, maintains the Qa and Qb in constant state, If S (Set) is pulsed high while R is held low, then the Qa output is forced high,and stays high even after S returns low; if R (Reset) is pulsed high while S is held

Dr. Clincy low, then the Qa output is forced low, and stays low even after R returns low. New Input Notice how the output feeds the input Flip Flops Previous State or Output Circuit Flip Flops - Sequential Circuits Previous State or Output Lecture Think of: Given R=0 and Qa=0, what can this be ? 4 Gated SR Latch or Flip Flop The time at which the latch is SET or RESET is controlled by a CLOCK input Called Gated SR Latch

Dr. Clincy Lecture 5 Gated D Latch Inputs S and R are derived from a single input D Clock pulse controls when the output is triggered Samples the D input at the time the clock is HIGH and stores that info until the next clock pulse Dr. Clincy During the time the clock is high, the input changed, causing the output toLecture change this is the problem 6 Potential Problem Thus far, the assumption has been the inputs S and R (or D) not changing while CLK is HIGH What would happen if S, R and/or D changed ? The output would change immediately This could be a problem To fix this (next ppt) Dr. Clincy During the time the clock is high, the input changed, causing the output toLecture change this is the problem 7

Two Flip Flop Use To Fix Clock Issue FF1 D Clock FF2 D Q Clk Q Qm D Q Clk Q Qs Q Q Use 2 D flip flops the FF2 clock is set to zero therefore, if there was a change in FF1 input, D, it wouldnt effect the FF2 Q value FF2 holds the value (a) Circuit Clock D Qm Q = Qs Clocks negative edge causes change (b) Timing diagram D

The arrow only symbolizes positive edge clock - the arrow with the NOT symbolizes negative edge clock Dr. Clincy Q Q (c) Graphical symbol Lecture If D changes while FF1 CLK is HIGH, Qm changes immediately Qs stays the same because FF2 CLK=0 Once the CLK goes LOW, FF2 reacts because its CLK=1 so it thens reflects D 8 T Flip Flop T Flip Flops are good for counters changes its state every clock cycle, if the input, T, is 1 Positive-edge triggered flip flop Since the previous state of Q was 0, it complements it to 1 Dr. Clincy Lecture 9 JK Flip Flop Combines the behavior of the SR and T flip flops First three entries are the same

behavior as the SR Latch (when CLK=1) Usually the state S=R=1 undefined for the JK Flip Flop, for J=K=1, next state is the complement of the present state Can store data like a D Flip Flop or can tie J & K inputs together and use to build counters (like a T flip flop) Dr. Clincy Lecture 10 Registers and Shift Registers A Flip Flop can store ONE bit in being able to handle a WORD, you will need a number of flip flops (32, 64, etc) arranged in a common structure called a REGISTER. All flip flops are synchronized by a common clock Data written into (loaded) flip flops at the same time Data is read from all flip flops at the same time F1 F2 F3 In Clock D Q Q D Q D Q Q Q F4 D

Q Out Q A simple shift register. Want the ability to rotate and shift the data Clock pulse will cause the contents of F1, F2, F3 and F4 to shift right (serially) To do a rotation, simply connect OUT to IN Dr. Clincy Lecture 11 Registers and Shift Registers Can load either serially or in parallel When clock pulse occurs, Serial shift takes place if Shift/Load=0 or if Shift/Load=1, parallel load is performed Dr. Clincy Lecture 12 Counters 3-stage or 3-bit counter constructed using T Flip Flops With T Flip Flips, when input T=1, the flip flop toggles changes state for each successive clock pulse Initially all set to 0 When clock pulse, Q0=1, therefore Q=0 disabling Q1 and Q1 disables Q2 (have 1,0,0) For the 2nd clock pulse, Q0=0, therefore Q=1, causing Q1=1 and therefore

Q=0 disabling Q2 (have 0,1,0) For the 3rd clock pulse, Q0=1, therefore Q=0 disabling Q2 and therefore disabling Q3 (have 1,1,0) Etc. LSB 000 001 Hmmm 010 011 100 Dr. Clincy 101 110 111 1 T Clock Q T Q Q T Q Q Q Q0 Q1 Q2

(a) Circuit Clock Q0 Q1 Q2 Count 0 1 2 3 4 5 6 7 0 (b) Timing diagram Figure A.35. A 3-bit up-counter. Lecture Called a Ripple Counter 13 Circuit Recall Combinatorial or Combinational Logic New Input Current State or output of the device is only affected by the

current inputs Current State or Output New Input Dr. Clincy Current State or Output Current State or output of the device is affected by the previous states Flip Flops Previous State or Output Circuit Sequential Logic Examples: Decoders Multiplexers Previous State or Output Lecture Examples: Shift Registers Counters 14 Sequential Circuit State Diagram If at 0 and x=0, count up to 1 (and

z=0) If x=0, count up, x=0 z=0 If x=1, count down S0 If at 0 and x=1, count down to 3 (and z=0) S1 Interested when 2 is realized z=1 when reach 2, else z=0 x=1 z=0 x = 1 z= 0 x = 0 z= 0 x=0 z=0 x = 1 z= 1 x=1 z=0 S3 S2 x = 0z = 1 State diagram of a mod-4 up/down counter that detects the count of 2. Dr. Clincy Lecture State diagram describes the functional behavior without any reference to

implementation15 Sequential Circuit State Table x=0 z=0 S 0 S1 x=1 z=0 x=1 z=0 x=0 z= 0 Can represent the info in the state diagram in a state table x=0 z=0 x=1 z=1 x=1 z=0 S3 x =0 z =1 Next state Output z x =0 x= 1 x =0 x= 1 S0 S1 S3 0

0 S1 S2 S0 0 0 S2 S3 S1 1 1 S3 S0 S2 0 0 Figure A.48. State table for the example of the up/down counter. S 2 State diagram of a mod-4 up/down counter that detects the count of 2. Dr. Clincy

Present state Present state Ne xt state x =0 x= 1 y2 y1 Y2 Y1 Y2 Y1 0 0 0 1 0 1 Outputz x=0 x= 1 1 1 0 0 1 0 0 0 0 0 1 0

1 1 0 1 1 1 1 1 0 0 1 0 0 0 Figure A.49. Lecture State assignment for the example in Figure A.48. 16 Sequential Circuit Equation Inputs y2,y1,x Outputs Y2, Y1 Present state Outputz x =0 x= 1 x=0 x= 1

y2 y1 Y2 Y1 Y2 Y1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0

0 Figure A.49. Dr. Clincy Ne xt state State assignment for the example in Figure A.48. Lecture 17 Sequential Circuit Circuit Design D Flip Flops used to store values of the two state variables between clock pulses Output from Flip Flops is the present-state of the variables Dr. Clincy Input, D, of the Flip Flops is the next-state of the variables Lecture 18 Finite State Machine Model The example we just implemented is an example of a Finite State Machine - is a model or abstraction of behavior composed of a finite number of states, transitions between those states, and actions Input x

Output z y1 Combinational logic y2 Y1 Y2 Present state Next state Delay elements (flip-flops) Figure A.52. Dr. Clincy Lecture A formal model of a finite state machine. 19