# DIGITAL ELECTRONICS. Counters. By: Electrical Engineering Department

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1 Counters By: Electrical Engineering Department 1

2 Counters Upon completion of the chapter, students should be able to:.1 Understand the basic concepts of asynchronous counter and synchronous counters, and the difference between them..1.1 Draw circuit and Timing Diagram of Asynchronous Counters.1.2 Interpret the Operation and Application of an asynchronous counter.1.3 Draw circuit and timing diagram of synchronous counters.1.4 Interpret the operation and application of synchronous up/down counters..1.5 Describe how the counters in.1.1 and.1.3 can be connected in cascade to produce higher mod.1.6 Explain the application of counters in Digital Clock

3 Introduction COUNTERS A counter is a register that goes through a predetermined sequence of states upon the application of clock pulses. Asynchronous counters Synchronous counters Asynchronous Counters (or Ripple counters) the clock signal (CLK) is only used to clock the first FF. Each FF (except the first FF) is clocked by the preceding FF. Synchronous Counters, the clock signal (CLK) is applied to all FF, which means that all FF shares the same clock signal, thus the output will change at the same time.

4 Introduction COUNTERS Modulus (MOD) the number of states it counts in a complete cycle before it goes back to the initial state. Thus, the number of flip-flops used depends on the MOD of the counter (ie; MOD-4 use 2 FF (2-bit), MOD-8 use 3 FF (3-bit), etc..) Example: MOD-4 Ripple/Asynchronous Up-Counter.

5 Asynchronous Counters

6 Asynchronous (Ripple) UP Counters The Asynchronous Counter that counts 4 number starts from and back to 00 is called MOD-4 Ripple (Asynchronous) Up-Counter. Next state table and state diagram Present State Next State 00 Q 1 Q 0 Q 1 Q

7 Asynchronous (Ripple) UP Counters Figure.1 : MOD 4 Asynchronous Up Counter A two-bit asynchronous counter is shown on the left. The external clock is connected to the clock input of the first flip-flop (FF0) only. So, FF0 changes state at the falling edge of each clock pulse, but FF1 changes only when triggered by the falling edge of the Q output of FF0. Note that for simplicity, the transitions of Q0, Q1 and CLK in the timing diagram above are shown as simultaneous even though this is an asynchronous counter. Actually, there is some small delay between the CLK, Q0 and Q1 transitions. Waveform

8 Asynchronous (Ripple) UP Counters Figure.1 : MOD 4 Asynchronous Up Counter Because of the inherent propagation delay through a flip-flop, the transition of the input clock pulse and a transition of the Q output of FF0 can never occur at exactly the same time. Therefore, the flip-flops cannot be triggered simultaneously, producing an asynchronous operation. The 2-bit ripple counter circuit shown has four different states, each one corresponding to a count value. Similarly, a counter with n flip-flops can have 2 to the power n states. (2 n ) The number of states in a counter is known as its mod (modulo) number. Thus a 2-bit counter is a mod-4 counter. Waveform

9 Asynchronous (Ripple) UP Counters Figure.1 : MOD 4 Asynchronous Up Counter Usually, all the CLEAR inputs are connected together, so that a single pulse can clear all the flip-flops before counting starts. The clock pulse fed into FF0 is rippled through the other counters after propagation delays, like a ripple on water, hence the name Ripple Counter A mod-n counter may also described as a divide-by-n counter. This is because the most significant flip-flop (the furthest flip-flop from the original clock pulse) produces one pulse for every n pulses at the clock input of the least significant flip-flop (the one triggers by the clock pulse). Waveform

10 MOD 8 Asynchronous Up Counter Figure.2 : MOD 8 Asynchronous Up Counter The following is a three-bit asynchronous binary counter and its timing diagram for one cycle. It works exactly the same way as a two- bit asynchronous binary counter mentioned above, except it has eight states due to the third flip-flop. Waveform 1

11 MOD 8 Asynchronous Up Counter Figure.3a Next State Table Present State Next State CBA CBA Figure.3b State Diagram

12 Exercise : Figure.4 : MOD 8 Asynchronous Up Counter A B C 1 J Q 1 J Q 1 J Q CLK CLK CLK K Q K Q K Q CLK A 0 B 0 C 0 1

13 MOD 16 Asynchronous Up counter (Negative Triggered) Figure.5 : MOD 16 Asynchronous Up Counter 1

14 MOD 16 Asynchronous Up counter (Positive Triggered) Figure.6 : MOD 16 Asynchronous Up Counter Exercise : Draw a MOD 16 Asynchronous DOWN Counter (Negative Triggered) : 1

15 Asynchronous DOWN Counter Figure.7 : MOD 4 or 2-bit Asynchronous down counter A (LSB) B (MSB) 1 J Q 1 J Q CLK CLK K Q K Q CLK A B Binary

16 Asynchronous Counters Exercise: Design a MOD-4 ripple down-counter Design a MOD-8 ripple down counter using negative triggered. Design a MOD-16 ripple down counter using positive triggered. 1

17 Asynchronous Counters (MOD 2 N ) So far, we have design the counters with MOD number equal to 2 N, where N is the number of bit (N = 1,2,3,4.) (also correspond to number of FF) Thus, the counters are limited on for counting MOD-2, MOD4, MOD-8, MOD-16 etc.. The question is how to design a MOD-5, MOD-6, MOD-7, MOD-9 which is not a MOD-2 N (MOD 2 N )? MOD-6 counters will count from 0 10 (000 2 ) to 5 10 (101 2 ) and after that will recount back to 0 10 (000 2 ) continuously. 1

18 Asynchronous Counters (MOD 2 N ) MOD-6 ripple up-counter (MOD 2 N ) Present St. Next St. CBA CBA (110) Figure.8b :State Diagram 1 2 Figure.8a :Next State Table Reset the state to when is detected 1

19 Asynchronous Counters (MOD 2 N ) Circuit diagram for MOD-6 ripple up-counter (MOD 2 N ) A (LSB) B C(MSB) Present St. Next St. CBA CBA (110) J Q J Q CLK CLR CLK K Q CLR CLK K Q J CLR K Q CLK Q Detect the output at CBA=110 to activate CLR. NAND gate is used to detect outputs that generates 1!

20 Asynchronous Counters (MOD 2 N ) Exercise : Draw MOD-5 Ripple Down-counter and Up- counter (MOD 2 N ) 2

21 IC for Asynchronous counters (IC 74293) IC for Asynchronous counter with Reset (MR1 and MR2) MR MR2 Q3 Q2 Q1 CP1 CP0 Q0 CP0 CP1 MR1 MR2 Q0 Q1 Q2 1 J Q 1 J Q 1 J Q 1 J Q CLK CLK CLK CLK K CLR Q K K Q CLR CLR Q K CLR Q Q3 2

22 IC for Asynchronous counters (IC 74293) Using IC to design MOD 16 Asynchronous UP-Counter! Exercise: Use IC to design MOD-10 ripple upcounter MR1 MR CP1 CP0 Q3 Q2 Q1 Q

23 IC for Asynchronous counters (IC 74293) Exercise: Determine the MOD for each configuration shown below? MR1 MR CP1 CP0 Q3 Q2 Q1 Q0 Answer : MOD 8 MR1 MR CP1 CP0 Q3 Q2 Q Q0 Answer : MOD 5 2

24 IC for Asynchronous counters (IC 74293) Determine the MOD for configuration shown below? MR1 MR CP1 CP0 Q3 Q2 Q1 Q Answer : MOD

25 IC for Asynchronous counters (IC 74293) CASCADE connection to produce Higher Mod Exercise : Design Asynchronous counters MOD-60 using IC Solution : Discuss with your Lecturer in class. Exercise : i. Design Asynchronous counters MOD-55 using IC ii. Design Asynchronous counters MOD using IC

26 Asynchronous Decade Counters Figure.3 : Asynchronous Decade Counter The binary counters previously introduced have two to the power n states. But counters with states less than this number are also possible. They are designed to have the number of states in their sequences, which are called truncated sequences. These sequences are achieved by forcing the counter to recycle before going through all of its normal states. A common modulus for counters with truncated sequences is ten. A counter with ten states in its sequence is called a decade counter. The circuit below is an implementation of a decade counter. 2

27 Asynchronous Decade Counters The sequence of the decade counter is shown in the table below: Once the counter counts to ten (1010), all the flip-flops are being cleared. Notice that only Q1 and Q3 are used to decode the count of ten. This is called partial decoding, as none of the other states (zero to nine) have both Q1 and Q3 HIGH at the same time. Figure.4 : True Table Asynchronous Decade Counter 2

28 Asynchronous Up-Down Counters Figure.5 : Asynchronous Up-Down Counter In certain applications a counter must be able to count both up and down. The circuit below is a 3-bit up-down counter. It counts up or down depending on the status of the control signals UP and DOWN. When the UP input is at 1 and the DOWN input is at 0, the NAND network between FF0 and FF1 will gate the non-inverted output (Q) of FF0 into the clock input of FF1. Similarly, Q of FF1 will be gated through the other NAND network into the clock input of FF2. Thus the counter will count up. 2

29 Asynchronous Up-Down Counters Figure.5 : Asynchronous Up-Down Counters When the control input UP is at 0 and DOWN is at 1, the inverted outputs of FF0 and FF1 are gated into the clock inputs of FF1 and FF2 respectively. If the flip-flops are initially reset to 0's, then the counter will go through the following sequence as input pulses are applied. 30

30 Asynchronous Up-Down Counters Notice that an asynchronous up-down counter is slower than an up counter or a down counter because of the additional propagation delay introduced by the NAND networks. 3

31 Asynchronous Up-Down Counters Figure.3 : Asynchronous Up-Down Counters Waveform For 4 Bit Up-Down Counter 3

32 Asynchronous Counters Disadvantages of Asynchronous Counters:- Propagation delay is severe for larger MOD of counters, especially at the MSB. Existence of glitch is inevitable for MOD 2 N counters. Cannot design random counters (i.e:- to design circuit that counts numbers in these sequence ) Solution, use SYNCHRONOUS COUNTERS. 3

33 Synchronous Counters 3

34 Synchronous Counters A synchronous counter, in contrast to an asynchronous counter, is one whose output bits change state simultaneously, with no ripple. The only way we can build such a counter circuit from J-K flip-flops is to connect all the clock inputs together, so that each and every flip-flop receives the exact same clock pulse at the exact same time: 3

35 Synchronous Counters Now, the question is, what do we do with the J and K inputs? We know that we still have to maintain the same divide-by-two frequency pattern in order to count in a binary sequence, and that this pattern is best achieved utilizing the "toggle" mode of the flip-flop, so the fact that the J and K inputs must both be (at times) "high" is clear. However, if we simply connect all the J and K inputs to the positive rail of the power supply as we did in the asynchronous circuit, this would clearly not work because all the flip-flops would toggle at the same time: with each and every clock pulse! 3

36 Synchronous Counters 3

37 Synchronous Counters 3

38 How To Design Synchronous Counter For synchronous counters, all the flip-flops are using the same CLOCK signal. Thus, the output would change synchronously. Procedure to design synchronous counter are as follows:- STEP 1: Obtain the State Diagram. STEP 2: Obtain the Excitation Table using state transition table for any particular FF (JK or D). Determine number of FF used. STEP 3: Obtain and simplify the function of each FF input using K-Map. STEP 4: Draw the circuit. 3

39 How To Design Synchronous Counter Design a MOD-4 synchronous up-counter, using JK FF. STEP 1: Obtain the State transition Diagram Binary

40 How To Design Synchronous Counter STEP 2: Obtain the Excitation table. Two JK FF are used. Present State OUTPUT TRANSITION FF INPUT Q N Q N+1 J K X X 1 0 X X 0 Excitation table Next State Input, J K B A B A J B K B J A K A X 1 X X X X 0 1 X X 1 X 1 4

41 How To Design Synchronous Counter STEP 3: Obtain the simplified function using K-Map A B X X A B X J B = A 1 1 X J A = 1 A B X X A B X 1 1 X 1 K B = A K A = 1 4

42 How To Design Synchronous Counter STEP 4: Draw the circuit diagram. A (LSB) B (MSB) 1 J A Q A CLK J B Q B CLK K A QA K B QB (MOD-4 synchronous up-counter ) 4

43 How To design Synchronous Counter Let us employ these techniques to design a MOD-8 counter to count in the following sequence: 0, 1, 2, 3, 4, 5, 6, 7. Step1: Determined Flip Flop Used and Creating state transition diagram. diagram. (Rajah Keadaan) N = 2 n 8 = 2 n n = log 8 / log 2 = 3 Flip Flop ( 3 Bit ) M = 2 n -1 = = 8-1 = 7 N = Modulo/MOD n = Flip Flop Used M = Maximum Number To Be Count 4

44 How To design Synchronous Counter Step 2: Creating present state-next state table Present State Next State Q 2 Q 1 Q 0 Q 2 Q 1 Q Q0 = QA Q1 = QB Q2 = Qc

45 How To Design Synchronous Counter Step 3: Expand the present state-next state table to form the transition table. Excitation Table (Jadual Ujaan Flip Flop _ JK) Q Q J K X X 1 0 X X 0 X indicates a "don t t care" condition. Present Next State Present inputs State Q C Q B Q A Q C Q B Q A J C K C J B K B J A K A X 0X 1X X 1X X X X0 1X X X1 X X0 0X 1X X0 1X X X0 X0 1X X1 X1 X1 4

46 How To Design Synchronous Counter Step 4: Use Karnaugh maps to identify the present state logic functions for each of the inputs. E.g. for J 2 we get: QA QA QcQB QcQB X X X X J C = Q B Q A Using similar techniques for the other inputs we get: K = Q C B Q A J B = Q A K = Q B A J A = 1 K = 1 A 4

47 How To Design Synchronous Counter Step 5: Constructing Circuit A A B B C C A A B B C C 4

48 How To Design Synchronous Counter that count Random number Example : Design a Synchronous Counter to Count 4,7,3,0 and 2 respectively using JKFlip Flop negative trigered by showing: i. Flip Flop Used ii. State Transition Diagram iii. Exitation Table / Present state, next State iv. Karnough Map & perform Simplified Function v. The Synchronous Counter

49 Synchronous Counter to Count 4,7,3,0 and 2 respectively Solution: Step 1 : Flip Flop Used Find Modulo, N= 2 n M = 7, M = 2 n -1 = 7 2 n = N, so, N = 7+1 = 8, MOD 8 2 n = 8, n = log 8 / log 2 n = 3 bit = 3 Flip Flop.

50 Synchronous Counter to Count 4,7,3,0 and 2 respectively Solution: Step 2 : State Transation Diagram, to count 4, 7, 3, 0 and Exitation Truth Table For Counter using JK FlipFlop Present Qn Next State Qn+1 J K x x x x 0

51 Synchronous Counter to Count 4,7,3,0 and 2 respectively Step 3 : Exitation Table /present State, Next State Deci Present Next State JC KC JB mal State KB JA KA QC QB QA QC QB QA x 0 1 x 1 x x 1 x 0 x x x 1 x x 1 x 0 x x x 1 0 x

52 Synchronous Counter to Count 4,7,3,0 and 2 respectively Step 4: Karnough Map and Simplified Function CB A x x x x x K-Map For JA = QC

53 Synchronous Counter to Count 4,7,3,0 and 2 respectively K-Map For JA = QC K-Map For KA = QC CB CB A X 1 A 0 X X X X X X X X X 1 0 X

54 Synchronous Counter to Count 4,7,3,0 and 2 respectively K-Map For JB = 1 K-Map For KB = QC CB CB A 0 1 X X 1 A 0 X 1 X X X X X X X 1 0 X

55 Synchronous Counter to Count 4,7,3,0 and 2 respectively K-Map For JC = QA+QB K-Map For KC = QB CB CB A X X A 0 X X X X 0 X X X X 1 X

56 Synchronous Counter to Count 4,7,3,0 and 2 respectively Step 5 : Perform Counter Circuit By using simplified function from K-Map, JA = QC, JB = 1, KB = QC, JC = QA + QB, KC = QB '1' / Vdd KA = QC, J A Q A JB QB JC QC K A Q A KB QB KC QC CP, CP,CLOCK CLOCK PULSE

57 Synchronous Counter Exercises: Design a counter to count in the following sequence: 6, 4. 2, 3, 1. Design a counter to count in the following sequence: 15,9,11,5,2,13,1. Do more exercises in Past Years Exam Paper. End Of This Topic.. 5

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