CHAPTER 6 COUNTERS & REGISTERS
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1 CHAPTER 6 COUNTERS & REGISTERS 6.1 Asynchronous Counter 6.2 Synchronous Counter 6.3 State Machine 6.4 Basic Shift Register 6.5 Serial In/Serial Out Shift Register 6.6 Serial In/Parallel Out Shift Register 6.7 Parallel In/Serial Out Shift Register 6.8 Parallel In/Parallel Out Shift Register
2 Lecture Outcomes At the end of this chapter student should be able to:- Differentiate the different type of counters Understanding the basic design steps to design any type of counters Differentiate between Moore & Mealy Machine (FSM) Understanding the FSM design steps (Moore/Mealy) Differentiate between various type of registers available (SISO/SIPO/PISO/PIPO) Understanding the registers design steps
3 6.1 Asynchronous Counter Revision: The rule to determine the number of FF is Example: Design a MOD-8 asynchronous counter. No of JK flip-flop = antilog 2 8 = 3 To build this counter, two ICs (contains 2 JK flipflops) are used.
4 The circuit connection for MOD-8 using ICs is J,K = 1 for toggle operation PRE, CLR = 1 for synchronisation
5 Counter with MOD number other than 2 n Example : Design a MOD-10 Counter There are 4 steps involved: 1. Determine the number of JK flip-flops needed 2. Determine the reset logic 3. Draw the block diagram 4. Circuit implementation.
6 Step 1 :Determine the number of JK flip-flops needed For MOD 10 (a.k.a. Decade Counter) Number 10 (decimal) in binary is there are 4 bits It requires 4 JK flip-flops
7 Step 2 :Determine the reset We know that 4 JK flip-flops is actually used in building MOD 16 (i.e. from 0000 to 1111). Thus, to make these 4 flip-flops to act as a MOD 10 (i.e. counting from 0000 to 1001), a reset circuitry is added. after it reaches 1001, the reset circuit is ON and JK flip-flops are cleared using CLR.
8 Maximum number of MOD-10 counter is 9. After 9 10 (1001) is number (1010) QB and QD are 1 s. RESET happens only when both QB and QD are HIGH AND configuration however, CLR is an active-low input, invert AND configuration NAND gate
9 Step 3 :Draw the block diagram The block diagram of MOD 10 counter is reset part
10 The waveform of MOD 10 counter is The glitch is due to the output is becoming 1010 for a short period of time before CLR. The delay in setting CLR is due to propagation delay of the NAND gate.
11 Step 4 :Circuit Implementation Circuit is implemented using 2 ICs of 74112
12 We could also implement a MOD-10 counter using IC (contains 4 JK flip-flops) Need to be connected externally
13 MOD 10 circuit implementation using IC 74293
14 Count-down Asynchronous Counter So far, all the counters are count-up counter. To implement count-down counter, the connection needs to be modified. 1. CLK pulses are supplied by Q 2. The Q A, Q B etc are taken from Q output. Example: MOD 8 count-down type counter
15 The waveform for MOD 8 count down counter is
16 6.2 Synchronous Counter Main problem of asynchronous counter is delay Due to the signals are rippled from one flip-flop into another Synchronous counter (a.k.a Parallel Counter) This synchronous counter has a common clock signal outputs change at the same time The inputs J & K need to be controlled so that they are toggled at specific time only. To do this, need to examine the counting steps table.
17 Example : MOD 16 Synchronous Counter COUNT Q D (MSB) Q C Q B Q A (LSB) Q A always toggle J1,K1 = 1 Q B always toggle at triggering edge when Q A =1 J2,K2 = Q A. Q C always toggle at triggering edge when Q A & Q B = 1 J3,K3 = Q A Q B. Q D always toggle at triggering edge when Q A & Q B & Q C = 1 J4,K4 = Q A Q B Q C.
18 Therefore, the circuit for MOD 16 synchronous counter is Q A Q A Q B Q C 1 Q A Q B
19 Synchronous Counter with MOD number other than 2 n Use asynchronous input CLR to reset the counter. Example: MOD 10 synchronous counter Same as MOD 10 asynchronous counter, i.e. Q D & Q B are 1 s.
20 Presettable Synchronous Counter Many synchronous counters (ICs) are presettable they can be preset to any desired starting count either asynchronously or synchronously. this operation is also called PARALLEL LOADING To load the counter with any desired count at one time: 1. Apply the desired count to the parallel inputs 2. Apply a LOW pulse to the PARALLEL LOAD input, PE
21 Example: 4-bit Presettable Synchronous Counter is Parallel inputs are P0, P1, P2 & P3. The NAND gates connected to them act as enable gate. What would be the counter s output if the PE is hold at low and the values of P0, P1, P2 & P3 are 1, 1, 0 & 0 respectively?
22 Count-down Synchronous Counter In section 6.1, the count-down counter is modified from the count-up counter. From these, we can design an up/down counter
23 6.3 State Machine State machine (also called as a sequential circuit) can be viewed as a synchronous counter with irregular sequence. There two types of state machines: 1. Moore machine Next state (output) depends on the present internal state only. 2. Mealy machine Next state (output) depends on the present internal state and also input at that particular of time.
24 Design of a state machine 1. State diagram A diagram that shows all the transition of states when clock is triggered. Number of FF = number of bits 2. Next state table Listing of all the present state along with its next state. 3. Excitation table Listing of all the JK connections of all FFs for the next state transition to occur. 4. K-map Determine the simplified logic expression for all J & K 5. Circuit implementation
25 Moore Machine Example: Design a 3-bit counter with this sequence,000,001,011,010,110,111,101,100,000, Solution STEP 1: State diagram Since this is a 3-bit counter 3 JK flip-flops are needed.
26 STEP 2: Next state table The present state is arranged in incremental binary counting order although the sequence of the counter is not.
27 STEP 3: Excitation table By referring to JK flip-flop transition table The excitation table is:
28 STEP 4: K-map
29 STEP 5: Circuit Implementation
30 Mealy Machine The present output from Mealy state machine depends on both the present input and the previous output. Thus, the present input needs to be considered too. Example: Design an up/down 3-bit Gray code counter. If input Y is low, the counter will perform count down operation else the counter will perform count up operation.
31 Solution STEP 1: State diagram Since this is a 3-bit counter 3 JK flip-flops are needed.
32 STEP 2: Next state table The present state is arranged in incremental binary counting order although the sequence of the counter is not.
33 STEP 3: Excitation table The excitation table is: (refer to JK FF transition table) Present State Input Next state C FF B FF A FF QC QB QA Y QC QB QA JC KC JB KB JA KA X 0 X 0 X X 0 X 1 X X 0 X X X 1 X X X X 0 1 X X X 0 0 X X X 1 X X X 0 X X 0 0 X 1 X X 1 0 X 0 X X 0 1 X X X 0 0 X X X 1 X 0 0 X X 0 X 0 1 X X 0 X 0 X X 0 X 1 X 0
34 STEP 4: K-map For C flip-flop J C = Q B Q A Y + Q B Q A Y =Q A (Q B Y) K C Q C Q B Q A Y 00 X X X X X X X X 0 0 J C Q B Q A Y Q B Q A Y Q C Q B Q A Y X X Q B Q A Y X X X X X X Q B Q A Y K C = Q B Q A Y + Q B Q A Y =Q A (Q B Y)
35 STEP 4: K-map (cont.) For B flip-flop J B = Q C Q A Y + Q C Q A Y =Q A (Q C Y) K B Q C Q B Q A Y 00 X 0 0 X Q C Q A Y Q C Q A Y J B Q C Q B Q A Y 00 0 X X X X X X X X 1 01 X 0 0 X 11 X 0 1 X 10 X 1 0 X Q C Q A Y Q C Q A Y K B = Q C Q A Y + Q C Q A Y =Q A (Q C Y)
36 STEP 4: K-map (cont.) For A flip-flop J A = Q C Q B Y + Q C Q B Y + Q C Q B Y + Q C Q B Y = Q C Q B Y J A Q C Q B Q A Y X X X X K A Q C Q B Q A Y 00 X X X X 01 X X X X X X X X K A = Q C Q B Y + Q C Q B Y + Q C Q B Y + Q C Q B Y = Q C Q B Y
37 STEP 5: Circuit Implementation
38 Register A register is a digital circuit with two basic functions: data storage } memory device data movement. } shift capability in transferring data The concept of data storing in D flip-flop When a 1 is on D, Q becomes a 1 at the rising edge of CLK. When the 1 on D is removed, Q still remains high (1). The storage capacity of a register is the total number of bits of data it can retain.
39 6.4 Basic Shift Register A shift register is a register in which the stored data can be shifted to the left or right. or a group of flip-flops arranged so that the binary numbers stored in the flip-flops are shifted from one flip-flop to the next for every clock cycle (ref: Tocci). Important in applications involving the storage and transfer of data.
40 There are several types of data movement in shift registers Serial In/Serial Out SISO Rotate left Rotate right
41 More on types of data movement in shift registers Parallel In/Serial Out PISO Serial In/ Parallel Out SIPO Parallel In/ Parallel Out PIPO
42 6.5 Serial In/Serial Out (SISO) Shift Register SISO register receives data serially, shift it and then output the data serially. The shift operation may be a shift right or left or both depending on the design.
43 4-bit SISO register (right shift) 4-bit register 4 D flip-flops (with PGT edge trigger) A FF B FF C FF D FF The first data is input to the A FF. Then, the data is moved to B FF followed by C FF before it finally reach D FF meaning 4-bit register takes 4 clock cycles to store 4-bits data.
44 4-bit SISO (right shift): storing operation Say, binary data of 1001 are to be stored in the SISO. Initially, the register is cleared (i.e. it contains 0000) At the FIRST rising edge of clock pulse, The LSB (1) is entered first because this is a right shift SISO.
45 At the SECOND rising edge of clock pulse, At the THIRD rising edge of clock pulse, At the FOURTH rising edge of clock pulse,
46 Now, all the bits are stored in this register. They are stored for any length of time as long as the flip-flops have dc power.
47 4-bit SISO (right shift): getting back the data Previously, binary data of 1001 are stored in the SISO. To get these data out, new 4-bit data (say, 0000 to clear the register) need to be entered. Data is read at Q D. The LSB is already at Q D.
48 At the FIRST (or FIFTH) rising edge of clock pulse, At the SECOND (or SIXTH) rising edge of clock pulse, At the THIRD (or SEVENTH) rising edge of clock pulse, Now, a complete set of data has been retrieved
49 Though the data have been completely retrieved, the register is not completely cleared yet. Q D still retains the MSB of the data. At the FOURTH (or EIGHTH) rising edge of clock pulse, Now, all the flip-flops are cleared. From here, we can see that it takes 8 clock cycles to completely clear the register.
50 6.6 Serial In/Parallel Out (SIPO) Shift Register SIPO register receives data serially, shift it and then output the data in parallel manner. In parallel output register, the output of each stage is externally accessible. Once the data are stored, each bit appears on its respective output line.
51 4-bit SIPO register 4-bit register 4 D flip-flops (with PGT edge trigger) A FF B FF C FF D FF The first data is input to the A FF. Then, the data is moved to B FF followed by C FF before it finally reach D FF meaning 4-bit register takes 4 clock cycles to store 4- bits data.
52 Operation of SIPO In storing operation, refer to SISO (as the data are stored in the same manner) Initially, the register is cleared (i.e. it contains 0000) At the FIRST rising edge of clock pulse, Here, LSB (1) is entered first.
53 At the SECOND rising edge of clock pulse, At the THIRD rising edge of clock pulse,
54 At the FOURTH rising edge of clock pulse, Now, a complete set of data has been stored. It will remain in this register until a dc power is turned off or the clock pulse is applied. At the same time, the data stored in this register can be retrieved.
55 74LS164: 8-bit SIPO shift register
56 The internal circuitry of the IC is: Questions: 1. If MSB is entered first, which of the output is the MSB after the 8 th clock cycle? 2. How to use this IC as a SISO?
57 6.7 Parallel In/Serial Out (PISO) Shift Register Parallel in allows a complete set of data to be entered at one time. PISO register receives data in parallel manner and then output the data in serial manner (shifting operation is done in between). PISO has a SHIFT/LOAD to set the operation mode.
58 4-bit PISO register 4-bit register 4 D flip-flops (with PGT edge trigger) A FF B FF C FF D FF The data are loaded to the A, B, C and D FFs simultaneously. SHIFT/LOAD input line is used to select the mode of the register.
59 Operation of PISO When SHIFT/LOAD is LOW Data are loaded into the respective FFs at the triggering edge (as AND gates of 1,3,5 & 7 are enabled). HIGH Data are shifted from one FF to the next at a triggering edge (as AND gates of 2,4 & 6 are enabled).
60 74LS165: 8-bit PISO shift register Clocking is provided through 2-input OR gate, where one input is used as a clock-inhibit function. The function of this IC is Inputs SH/LD CP CP INH Operation L X X Parallel load H H X No change H X H No change H L Shifting H L Shifting
61 The internal circuitry of the IC is: Question: How to use this IC as a SISO?
62 6.8 Parallel In/Parallel Out (PIPO) Shift Register PIPO allows a complete set of data to be entered simultaneously and after a triggering edge, these data are ready to be read out. If you refer back to Chapter 1, parallel data transmission is faster than serial data transmission.
63 4-bit PIPO register 4-bit register 4 D flip-flops (with PGT edge trigger) A FF B FF C FF D FF The data are loaded to the A, B, C and D FFs simultaneously. The data are retrieved at Q A, Q B, Q C and Q D respectively.
64 74LS195: 4-bit PIPO shift register SHIFT/LOAD input line LOW the data on the parallel inputs are entered synchronously on PGT of the clock pulse HIGH the stored data will shift right (Q0 Q3) synchronously on PGT of the clock pulse Active-low CLR is asynchronous.
65 The internal circuitry of the IC is: Question: How to use JK inputs as a Serial Data In?
66
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