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ENGR 2720 Chapter 9 Counters and Shift Registers 1 Counters and Shift Registers • Counter: A Sequential Circuit that counts pulses. Used for Event Counting, Frequency Division, Timing, and Control Operations. • Shift Register: A Sequential Circuit that moves stored data bits in a specific direction. Used in Serial Data Transfers, Arithmetic, and Delays. 2 Counter Terminology • A Counter is a digital circuit whose outputs progress in a predictable repeating pattern. It advances one state for each clock pulse. • State Diagram: A graphical diagram showing the progression of states in a sequential circuit such as a counter. • Count Sequence: The specific series of output states through which a counter progresses. • Modulus: The number of states a counter sequences through before repeating (mod-n). • Counter directions: – DOWN - count high to low (MSB to LSB) – UP - count low to high (LSB to MSB). 3 Counter Modulus • Modulus of a counter is the number of states through which a counter progresses. • A Mod-12 UP Counter counts 12 states from 0000 to 1011 (0 to 11 decimal). The process then repeats. • A Mod-12 DOWN counter counts from 1011 (to 0000 (11 to 0 decimal), then repeats. 4 State Diagram • A diagram that shows the progressive states of a sequential circuit. • The progression from one state to the next state is shown by an arrow. – (0000 0001 0010). • Each state progression is caused by a pulse on the clock to the sequential circuit. 5 MOD 12 Counter State Diagram • With each clock pulse the counter progresses by one state from its present position on the state diagram to the next state in the sequence. • This close system of counting and adding is known as modulo arithmetic. 6 Full-sequence Counter • An n-bit counter that counts the maximum modulus (2n) is called a full-sequence counter such as Mod 2, Mod 4, Mod 8, etc. • A 4-bit mod 16 UP counter that counts up from 0000 to 1111 is an example of a full-sequence counter. 7 Truncated Counter • An n-bit counter whose modulus is less than the maximum possible is called a truncated sequence counter, such as mod 3 (n = 2), mod 12 (n = 4). • A 4-bit mod 12 UP counter that counts from 0000 to 1011 is an example of a truncated counter 8 Counter Timing Diagram (Mod-16 Full-sequence Counter) • Shows the timing relationships between the input clock and the outputs Q3, Q2, Q1, …Qn of a counter. • For a 4-bit mod 16 counter, the output Q0 changes for every clock pulse, Q1 changes on every two clock pulses, Q2 on four, and Q3 on 8 clocks. • The outputs (Q0 Q3) of the counter can be used as frequency dividers with Q0 = clock 2, Q1 = clock 4, Q2 = clock 8, and Q3 = clock 16. 9 Counter Timing Diagram (Mod-12 Truncated Counter The outputs (Q0 Q3) of the counter can be used as frequency dividers with Q0 = clock 2, Q1 = clock 4, Q2 = clock 12, and Q3 = clock 12. 10 Synchronous Counters • A counter whose flip-flops are all clocked by the same source and change state in synchronization. • The memory section keeps track of the present state. • The control section directs the counter to the next state using command and status lines. Directs to next state Present state 11 Designing a Synchronous Counter 1. Define the problem. The circuit must count in binary sequence from 0000 to 1011. 2. Draw a state diagram 12 Step 3 Designing a Synchronous Counter Q Q Present State Next State J K Coments 0 0 0 X No change or reset 0 1 1 X Nochange or set 1 0 X 1 Toggle or set 1 1 X 0 Toggle or reset 13 Designing a Synchronous Counter Simplify the Boolean expression for each input 14 MOD-12 Synchronous Counter 15 Analysis of Synchronous Counters (Unknown Modulus) • Set equations for the (JK, D, T) inputs in terms of the Q outputs for the counter. • Set up a table similar to the one in Table 9.5 and place the first initial state in the present state column (usually all 000). • Use the initial state to fill in the Inputs that will cause this state on a clock pulse. • Determine the result on each FF in the counter and place this in the next state. • Enter the next state on the present state line 2 and repeat the process until you cycle back to the first initial state. 16 Analysis of Synchronous Counters (Unknown Modulus) 1. Set equations for the (JK, D, T) inputs in terms of the Q outputs for the counter. J2 = Q1Q0 J1 = Q0 J0 = Q2’ K2 = 1 K1 = Q0 K0 = 1 17 Analysis of Synchronous Counters (Unknown Modulus) 2. Set up the state table. Place the first initial state in the present state column (usually all 000). 3. Use the initial state to fill in the Inputs that will cause this state on a clock pulse. 4. Determine the result on each FF in the counter and place this in the next state. 5. Enter the next state on the present state line 2 and repeat the process until you cycle back to the first initial state. 18 State Table (Steps 2-5) J 2 = Q 1 Q0 J 1 = Q0 J 0 = Q2 ’ K2 = 1 K1 = Q0 K0 = 1 19 Analysis of Synchronous Counters (Unknown Modulus) 6. Draw the timing and state diagrams. 20 LPM Counters LPM (Library of Parameterized Modules) Counters: Refer to Chapter 9, Entering Simple LPM Counters with the Quartus II Block Editor. 21 Shift Register (SR) Terminology • Shift Register: A synchronous sequential circuit that will store and move n-bit data either serially or in parallel in a n-bit Register (FF). • Left Shift: A movement of data from right to left in the shift register (toward the MSB). One bit shift per clock pulse. • Right Shift: A movement of data from left to right in the shift register (toward the LSB). One bit shift per clock pulse. • Rotation: Serial shifting (right or left) with the output of the last FF connected to the input of the first. Results in continuous circulation of SR data. 22 Shift Register Terminology 23 4-bit Shift Register (Configured to Shift Right) 24 Right Shifting a “1” Through a Shift Register 25 Right Shifting “1s” to Fill a Shift Register 26 Left Shifting a “1” Through a Shift Register 27 Left Shifting “1s” to Fill a Shift Register 28 Bi-Directional Shift Register • Uses a control input signal called direction to change circuit function from shift right to shift left. • When DIR = 0, the path of Left_Shift_In is selected. • When DIR = 1, it selects the Right_ Shift_In Path. 29 SR with Parallel Load • Similar to a Parallel Load Counter, the Shift Register is shown in Figure 9.93. • Uses a 2-to-1 Mux (AND/OR) to control inputs to the FF in the SR. The input choice is from the previous FF Output or the Parallel Input. • When Load = 1, Parallel Data is loaded in on the next clock pulse. 30 Universal SR • Combines the basic functions of a Parallel Load SR with a Bi-Directional SR. • Uses Two Control Inputs (S1,S0) to select the function 31 Universal SR Truth Table (S1/S0) S 1 S 0 Function D3 D2 D1 D0 0 0 Hold Q3 Q2 Q1 Q0 0 1 Shif t Left Shift Right RSI * Q3 Q2 Q1 1 t Right 0 Shif Shift Left Q2 Q1 Q0 LSI ** 1 1 Load P3 P2 P1 P0 * RSI = Right-Shif t Input / ** LSI = Left-Shif t Input 32 LPM Shift Registers • Allows the use of a Programmable LPM shift register called lpm_shiftreg. • Has various required and optional parameters that are defined, such as LPM_WIDTH… (Table 9.16 in text). • Design approach is the same as for Counters using Structured VHDL. 33 Shift Register Counters • Two types: Ring and Johnson • Ring Counter: A serial Shift Register with feedback from the output of the last FF to the input of the first FF. • Counter sequences are based on a continuous rotation of data through the SR. 34 4- Bit Ring Counters • A basic Ring Counter is constructed of D-FF with a Feedback Loop. • Data is initially loaded into the SR by using either Resets or Presets. • The counter can circulate a 0 or 1 by loading a 1000 or 0111. • The Modulus of a Ring Counter is defined as the maximum number of unique states. • Modulus is dependent on the initial load value {1000, 0100, 0010, 0001} = Mod4 while {1010, 0101} = Mod2. • Typically an N-FF Ring Counter has N-States, not 2N like a binary counter. 35 Circulating a “1” in a Ring Counter 36 Circulating a “0” in a Ring Counter 37 Johnson Counters • Johnson Counter: A serial shift register with the complemented feedback from the output of the last FF to the input of the first FF. • Same as the Ring Counter sequences based on a continuous rotation of data through the SR. • Same as a Ring except that Q’ (Complement) is fed back to D3, not to Q0. • Adds a complement or “twist” to the data and is called a Twisted Ring Counter. • Usually Initialized with 0000 by a Clear. 38 Johnson Counters • Typically has more states than a ring counter. • Sequence of states = {0000, 1000, 1100, 1110, 1111, 0111, 0011, 0001}. • Maximum Modulus is 2n for a circuit with n flip-flops. 39 Data Circulating in a 4-bit Johnson Counter 40

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