EE201L Homework # One-Hot state assignment method of designing a state machine LRH = 000 BOTH LIGHTS OFF IDLE Q I Q R = 1 = 1000 Q L Q H

Size: px

Start display at page:

Download "EE201L Homework # One-Hot state assignment method of designing a state machine LRH = 000 BOTH LIGHTS OFF IDLE Q I Q R = 1 = 1000 Q L Q H"

Dustin McGee
5 years ago
Views:

1 EE201L Homework # 5 Instructor: G. Puvvada 1. One-Hot state assignment method of designing a state machine Consider the turn signals and hazard warning signal controls on most cars. The turn signal control lever has three positions: Left, Neutral, Right. Corresponding to the three positions, let us assume two coded signal outputs are available from the switch: L (for left) and R (for right) such that LR = 10 for left, 00 for neutral and 01 for right. Note: LR = 11 is not possible because of the lever construction. The hazard warning switch can be operated independently. H = 1 indicates the operation of this switch. The following state diagram representing the controller has four states as shown, ILE, LEFT, RIGHT, HAZAR. Four Flip-flops were assigned to the above states, I, L, R, H respectively. In the ILE state, both left and right lights are off and in the HAZAR state both the lights are on. Similarly in the LEFT state, the left light is on and in the RIGHT state the right light is on. The outputs are shown at the top of the state circle. FLASHING is achieved by going back to the ILE state from any other state unconditionally on the next clock. ~RE LRH = 000 LEFT LIGHT ON LEFT L = 1 I L R H = 0100 LRH = 1X0 LRH = XXX BOTH LIGHTS OFF ILE I = 1 I L R H = 1000 LRH = XXX LRH = XX1 LRH = LRH = RIGHT LIGHT ON RIGHT R = 1 I L R H = 0010 BOTH LIGHTS ON HAZAR H = 1 I L R H = If we want the lights to be ON for 1 second and OFF for 1 second, what should be the frequency of clock that runs the above state machine? 1.2 Complete the state diagram by filling state transition conditions. 1.3 Write down the next state equations. Hint: Consider all the arrows converging on a state to decide under what conditions that state becomes the next state. 8/21/18 EE201L Homework #5 1 / 15

2 I = I * = L = L * = R = R * = H = H * = 1.4 raw the NSL (NSL = Next State Logic). Besides the logic which drives the -inputs of all the flip-flops (which constitutes the core of the NSL), you should include asynchronous initialization logic/circuitry/connections which will establish the desired initial state when a lowactive reset (~RE) is active during the first few micro- or milliseconds after switching on power. I L R H 2. State diagram design: Consider the following three-road junction. One of the three roads is given GREEN signal (one road at a time) while other two roads are given RE signal. There is no YELLOW signal here. The three roads are equipped with sensors sensing presence of cars so that we can skip giving green signal to the road which has no cars waiting. S1 = 1 means that cars are present on road R1. 2/25/07 EE201L Homework #5 2 / 15

3 Specifications for the design: 1. uring busy hours when there are cars on all roads, (S1 = 1, S2 = 1, and S3 = 1), green signal shall be rotated in the simple order (i.e. R1 => R2 => R3 => R1...). Also when there are no cars on any of the three roads (S1 = 0, S2 = 0, and S3 = 0), we rotate the signal in simple order. 2. Suppose we are currently in R1 state. 2.1 If we are currently in R1 state, and if road#1 continues to need the signal (S1 = 1) and others do no need it (S2 = 0 and S3 = 0) (i.e. if S1S2S3 = 100), then you can retain R1 signal (remain in R1 state). 2.2 If we are currently in R1 state, if R2 needs the signal (S2 = 1), then no matter whether R1 needs or not, R3 needs or not (i.e. if S1S2S3 = X1X or 0X0), then we need to give R2 its legal turn. 2.3 If we are currently in R1 state, and if R3 needs the signal and R2 does not need it (no matter whether R1 continues to need the signal or not) (i.e. if S1S2S3 = X01), then we give the signal to R In the state diagram below, all the state transition arrows have been drawn. State transition conditions have been specified for 3 of the 9 state transition arrows. Complete the state diagram below by writing the transition conditions for the remaining six state transition arrows. R3 R3 S3 S2 S1S2S3 = X01 R1 S1 R2 ~RE S2.S3 S1.S2.S3 S1S2S3 = 100 R1 (S2 + S1.S3) S1S2S3 = X1X or 0X0 R2 2.2 Mutual exclusion and All inclusion properties: The conditions associated with the state transition arrows (diverging from / converging on to) a state should satisfy mutual exclusion. The conditions associated with the state transition arrows (diverging from / converging on to) a state should satisfy all inclusion. To verify mutual exclusion, we form (sum of pair products of the conditions / simple sum of the conditions) and check to see that it (the sum) always becomes a (zero / one). To verify all inclusion, we form (sum of pair products of the conditions / simple sum of the conditions) and check to see that it (the sum) always becomes a (zero / one). 2/25/07 EE201L Homework #5 3 / 15

4 2.3 Implementing the 3-state state machine using One-Hot state assignment: Complete the following implementation. Among the three pieces of the NSL (next state logic), you need to draw only the NSL associated with the state R1 (flip-flop producing R1). NSL NSL You do not have to complete this NSL PRE R3 SysClk PRE R1 NSL You do not have to complete this NSL PRE R2 2.4 If the 3-state state machine is to be implemented using encoded state assignment method (EE101 method), we need only two flip flops in the SM (State Memory) block. To design the NSL (Next State Logic) here, we need to draw (1/2/3/4) Karnaugh maps, each having (state a number) cells. State how you arrived at these two answers (use words/phrases such as /, etc). S1 S2 S3 0 1 NSL 0* 1* SM PRE PRE 0 1 2/25/07 EE201L Homework #5 4 / 15

5 3. Temperature control and State machine design: An Alaskan firm has designed the following room heater to control room temperature. The heater consists of two heating coils HC1 and HC2. It has three temperature sensors (switches) which produce three digital outputs N, L, and VL. N = 1 ==> Temperature is NORMAL (or above normal)>75 0 F L = 1 ==> Temperature is LOW (below normal) <70 0 F VL = 1==> Temperature is VERY LOW <65 0 F Obviously when VL is true (VL = 1), then L is also true (L = 1). Similarly when N is true (N = 1), both L and VL are false (L = VL = 0). It is possible that all three outputs read zero for example if the temperature is 72 0 F. If the temperature falls below the LOW mark (L = 1), the heating coil-1 (HC1) is switched on (HC1 = 1). If heating coil # 1 could not hold or raise the temperature and the temperature further falls to VERY LOW mark (VL = 1), the heating coil2 (HC2) is also switched on (HC2 = 1). Once any heating coil is switched on, it is only shut off when the temperature builds up to the NORMAL level. 3.1 Complete the following state diagram. All state transition arrows are already drawn. You need to complete the missing transition conditions. State I is the INITIAL state in which both coils are off (HC1, HC2 = 0, 0). State SH is the SINGLE-HEATER state in which only HC1 is on ( HC1, HC2 = 1, 0). State TH is the TWO-HEATER state in which both heaters are on (HC1, HC2 = 1, 1). ~Reset I HC1, HC2 = 0,0 N TH HC1, HC2 = 1,1 L VL N SH HC1, HC2= 1,0 2/25/07 EE201L Homework #5 5 / 15

6 3.2 Verify algebraically or logically using reason that the conditions associated with the three statetransition arrows diverging from the SH state satisfy the two necessary requirements (Note that N.VL = 0, as temperature can not be normal as well as very low) : MUTUALLY EXCLUSIVE: ALL INCLUSIVE: 3.3 Complete the following waveforms. The temperature switches (N, L, and VL) behaved in the way shown below based on the weather conditions. ~RE N L VL STATE I I SH TH HC1 HC2 2/25/07 EE201L Homework #5 6 / 15

7 3.4 Implement the state machine using one-hot method. o not forget to produce the output control HC1 and HC2 to control the heating coils. I TH SH Produce the output control HC1 and HC2 here. HC1 HC2 3.5 EE101 method of encoded state assignment: If this state machine was designed using the EE101 method of encoded state assignment, how many flip-flops are needed for the state memory? How many K-maps of what size (expressed in cells) are needed to complete the next state logic? K-maps, each of cells. Explain how you arrived at the above three answers Complete the State Transition Table below for the encoded state assignment method. Note: The table below includes outputs also. 2/25/07 EE201L Homework #5 7 / 15

8 NEXT STATE Current State N L VL N L VL N L VL N L VL OUTPUTS Symbolic Coded 1 0 Symbolic Coded 1* 0* Symbolic Coded 1* 0* Symbolic Coded 1* 0* Symbolic Coded 1* 0* HC2 HC1 I 0 0 I SH 0 1 I 0 0 TH 1 1 I 0 0 NONE 10 ANY XX ANY XX ANY XX ANY XX 0 0 Note: The remaining four combinations of N,L,VL (1,0,1; 1,1,0; 1,1,1; 0,0,1) are NOT possible. Hence they are not listed. 3.6 Show how you would produce the outputs HC2 and HC1. Comment on how or why the logic to produce HC2 and HC1 turned out to be so simple. 4. One-Hot method of state machine design: A dish washer (from MAYTAG?) has a cleaning sequence of three states Add water ==> Rinse ==> rain followed by a drying state (ry). The cleaning sequence (Add water => Rinse => rain) is repeated if, at the end of drain state, the cleanliness sensor (CS) indicates UNCLEAN status (CS = 0). Similarly the drying continues until the dryness sensor indicates RY status (S = 1). A slow clock of 1 cycle/ minute frequency is used to take the dish washer through its states. An incomplete state transition diagram is given below. Write the values of CS and S on the state transition arrows to complete it. CS= ~RE S= START = 0 A WATER CS= S= RINSE RAIN RY ONE START = 1 2/25/07 EE201L Homework #5 8 / 15

9 4.1 Complete the next state equations below: A-WATER = * A-WATER = RINSE = * RINSE = RAIN = * RAIN = RY = * RY = ONE = * ONE = Complete the one-hot design below. Add WATER AddWater RINSE RINSE RAIN RAIN ~RE RY ONE RY PRE ONE 2/25/07 EE201L Homework #5 9 / 15

10 Complete the waveforms below. 2/25/07 EE201L Homework #5 10 / 15 ONE RY RAIN RINSE A-WATER S CS START ~RE EE201L Homework #5 10/15 4.2

11 5. State machine design: Reproduced below is the PCH and RUR crossing traffic lights control state diagram from your homework # 1. In your homework, you implemented this control using the EE101 encoded state assignment method. Here, we are re-implementing the same using one-hot state assignment method. The complete state diagram of the problem has been shown below. PCHS2 ~RE S PCHS1 PCH-G PG = 1 RUR S2 S 0 1 S1 PCHN1 PCH-Y PY = RUR-Y RY = 1 PCHN2 PCH 1 2 RUR-G RG = 1 S +B S.B IFL S1 S2 S (RURAL TRAFFIC) PCHN1 PCHN2 PCHS1 PCHS2 B (Backup) 5.1 Complete the next state equations below (for one-hot state assignment): PCH-G = * PCH-G = PCH-Y = * PCH-Y = RUR-G = * RUR-G = RUR-Y = * RUR-Y = 2/25/07 EE201L Homework #5 11 / 15

12 5.2 Complete the implementation below using one-hot state assignment. (a) Complete the ~RE control to see that the PCH-G state is the initial state after switching on power to this unit. (b) Complete the NSL. (c) Complete the OFL (Output Function Logic) to produce the four outputs (lights) PG, PY, PR, RG, RY, and RR as a function of the current state, PCH-G, PCH-Y, RUR-G, and RUR-Y. Note: If it is neither GREEN nor YELLOW on PCH, it must be RE on PCH. SM+NSL PCH-G PCH-Y RUR-Y RUR-G OFL PCH-G PCH-Y PG (Green light on PCH) PY (Yellow light on PCH) RUR-G RUR-Y PR (Red light on PCH) RG (Green light on RUR) RY (Yellow light on RUR) RR (Red light on RUR) 2/25/07 EE201L Homework #5 12 / 15

13 5.3 Complete the following waveform for the above (one-hot) implementation. ~RE S B PCH-G STATE PCH-Y PCH-G PCH-Y RUR-G RUR-Y 6. Sprinkler system control by ONE-HOT method You need to control the sprinklers in the front and back yards of your club-house. Inputs to your system: RUN: comes from the user run switch WF: wetness sensor for the front yard WB: wetness sensor for the back yard States: ILE: You come into this state on power-on reset (when ~RE = 0). You remain here (or return here) if the RUN is off (RUN = 0). When RUN is on (RUN = 1), you may still remain here (or you will return here) if both the yards are wet (WF = 1 and WB = 1). SF: Sprinkle Front yard. SB: Sprinkle Back yard. Once you start sprinkling a yard, you will continue until it is wet enough, unless the RUN is cancelled by the user. The front yard has a little higher priority over the back yard in the sense, if the controller is in the idle state, and both the yards are dry, then we go to the SF state and sprinkle the front yard first. However, while sprinkling the back yard, even if the front yard dries up, we will not abruptly stop the back yard sprinkling. 2/25/07 EE201L Homework #5 13 / 15

14 6.1 Complete the state diagram. Write all state transition conditions. ~RE SF ILE SB 6.2 Complete the next state equations below: ILE = * ILE = SF = * SF = SB = * SB = 2/25/07 EE201L Homework #5 14 / 15

15 6.3 Using ONE-HOT design technique, complete the control unit design. V CC Run postion RUN Stop position SF ILE SB 6.4 Find the complexity of designing the same control unit using the EE101 encoded state assignment method. Here you would use two flip-flops (in the state memory) to represent the three states, ILE, SF, and SB. So, current state is two bits and the desired next state is also two bits. The inputs to the NSL (Next State Logic) are RUN, WF, and WB. We need to deal with K-Maps, each of cells to finish the NSL design. 2/25/07 EE201L Homework #5 15 / 15

EE201l Homework # 6. Microprogrammed Control Unit Design

EE201l Homework # 6. Microprogrammed Control Unit Design EE201l Homework # 6 Microprogrammed ontrol Unit Design Instructor: G. Puvvada 1. Refer to the design of the microprogrammed control unit for the change dispenser discussed in your class notes Assume that