Johnson Ring Counter: Definition and Basic Concept

A Johnson ring counter, also known as a twisted ring counter or Möbius counter, is a synchronous shift register with the inverted output of the last stage fed back into the input of the first stage. This feedback mechanism creates a circulating pattern of bits that distinguishes it from conventional ring counters.

Mathematical Foundation

The state sequence of an n-stage Johnson counter follows a predictable cyclic pattern with a modulus of 2n, double that of a standard ring counter. The state transitions can be described by:

where Q_i^t represents the state of the i-th flip-flop at time t.

Circuit Architecture

The canonical implementation consists of:

• D flip-flops connected in series (typically 4-8 stages)
• A feedback inverter between Q̅ of the last stage and D of the first
• Synchronous clock distribution to all flip-flops

Characteristic Waveforms

The output generates a quadrature phase relationship between stages, making it valuable for:

• Phase-shifted clock generation
• Digital signal sequencing in communication systems
• Mechanical position encoding (rotary encoders)

Key Advantages Over Standard Counters

Historical Context

First patented by Robert Royce Johnson in 1953 while at Sperry Gyroscope Company, the design emerged as a solution for reliable position encoding in early electromechanical navigation systems. Its inherent fault tolerance made it particularly valuable in aerospace applications.

1.2 Working Principle

The Johnson Ring Counter, also known as a twisted ring counter, is a synchronous shift register with feedback that generates a cyclic sequence of states. Unlike a standard ring counter, where the output of the last flip-flop feeds directly back to the input of the first, the Johnson counter inverts the feedback signal, resulting in a sequence length of 2N for an N-stage counter.

State Transition Mechanism

The counter operates by propagating a single high or low bit through a series of D-type flip-flops, with the complement of the final output fed back to the input. For a 4-stage Johnson counter (N=4), the sequence proceeds as follows:

Each clock pulse shifts the existing bits right and inserts the inverted last bit at the first stage. The complete 8-state sequence for a 4-stage counter is:

1. 0000 → 1000
2. 1000 → 1100
3. 1100 → 1110
4. 1110 → 1111
5. 1111 → 0111
6. 0111 → 0011
7. 0011 → 0001
8. 0001 → 0000 (cycle repeats)

Mathematical Basis

The state transitions follow Boolean logic, where for an N-bit counter, the next state S_n+1 is derived from the current state S_n as:

where ≫ denotes a right shift, | is bitwise OR, ∼ is inversion, and ≪ is a left shift. The modulus of the sequence is always 2N, providing higher state density than a standard ring counter (modulus N).

Timing and Synchronization

Since the Johnson counter is synchronous, all flip-flops update on the rising or falling edge of a shared clock signal. The propagation delay t_pd must satisfy:

where T_clock is the clock period and t_setup is the flip-flop setup time. Metastability can occur if this constraint is violated.

Applications

• Phase generators in quadrature modulation/demodulation systems, producing 4-phase (90° spaced) signals from a 2-stage counter.
• Sequence detectors in error-checking circuits, leveraging the predictable state transitions.
• Control logic for multi-phase clock domains, where each state enables a different subsystem.

1.3 Comparison with Other Shift Registers

The Johnson ring counter, while functionally similar to other shift registers, exhibits distinct differences in operation, efficiency, and application. Below, we compare it with three common shift register types: the serial-in serial-out (SISO), parallel-in parallel-out (PIPO), and the standard ring counter.

Serial-In Serial-Out (SISO) Shift Register

A SISO shift register processes data sequentially, with each bit shifted through the register one at a time. The Johnson counter, in contrast, recycles its output back to the input, creating a closed loop. While a SISO requires N clock cycles to load N bits, a Johnson counter with N flip-flops produces 2N distinct states, doubling its effective state space. This makes the Johnson counter more efficient for applications requiring repetitive pattern generation, such as in LED chasers or frequency dividers.

Parallel-In Parallel-Out (PIPO) Shift Register

PIPO registers allow simultaneous loading and reading of all bits, making them ideal for high-speed data transfer. However, they lack the Johnson counter's inherent state sequencing capability. The Johnson counter's ability to generate a continuous, non-repeating sequence of states (until all 2N states are exhausted) is advantageous in control systems where deterministic state transitions are critical, such as in stepper motor controllers.

Standard Ring Counter

A standard ring counter circulates a single '1' or '0' through its flip-flops, producing only N unique states for N flip-flops. The Johnson counter's modified feedback mechanism (inverting the output before feeding it back) doubles the number of states to 2N. This property is mathematically expressed as:

where S_Johnson is the number of unique states. The standard ring counter's state count remains:

Power and Area Efficiency

Johnson counters typically consume less power than PIPO registers due to reduced parallel data switching. However, they require more flip-flops than a SISO for equivalent state coverage. For example, a 4-bit Johnson counter (8 states) needs 4 flip-flops, while a 3-bit SISO (8 states) requires only 3. The trade-off between state density and hardware complexity must be evaluated based on application constraints.

Applications in Digital Systems

• SISO: Best for serial data buffering (e.g., UART communication).
• PIPO: Optimal for register files and CPU data paths.
• Johnson Counter: Preferred for quadrature signal generation and pseudo-random sequence generation in cryptographic systems.

2.1 Components Required

A Johnson Ring Counter, also known as a twisted ring counter, is a sequential logic circuit constructed using a shift register with an inverted feedback loop. The following components are essential for its implementation:

Primary Components

• D Flip-Flops (or JK Flip-Flops configured as D Flip-Flops) — The fundamental building blocks of the shift register. The number of flip-flops determines the counter's modulus (2N states for an N-stage counter).
• Clock Signal Source — A square-wave oscillator or pulse generator to synchronize state transitions. The frequency must comply with the flip-flops' setup/hold times.
• Inverter (NOT Gate) — Provides the feedback inversion characteristic of Johnson counters. Standard 74HC04 or CD4049 ICs are typical choices.

Supporting Components

• Power Supply — Typically +5V for TTL (e.g., 74LS series) or 3.3V–15V for CMOS (e.g., CD4000 series), depending on logic family.
• Decoupling Capacitors — 100nF ceramic capacitors placed near each IC's power pins to suppress high-frequency noise.
• Current-Limiting Resistors — For LED indicators (330Ω–1kΩ) if visual state monitoring is implemented.

Optional Enhancements

• Reset Circuitry — A pushbutton or logic-controlled reset to initialize the counter to a known state (e.g., 000...1).
• Prescaler — Frequency divider (e.g., 74HC390) to reduce clock speed for human observation.
• Output Buffers — 74HC245 or similar to drive heavy loads when interfacing with external systems.

Component Selection Criteria

Critical parameters for flip-flop selection include:

where t_su is the flip-flop setup time and t_{prop,feedback} is the cumulative propagation delay through the feedback path. For CMOS implementations, ensure:

where N is the number of stages and t_PHL/t_PLH are output transition times.

Practical Implementation Notes

For a 4-stage Johnson counter (8 unique states), the component count would be:

• 4× D Flip-Flops (e.g., 74HC175 quad flip-flop)
• 1× Inverter (1/6 of a 74HC04 hex inverter)
• 1× 555 Timer or crystal oscillator for clock generation

2.2 Circuit Diagram and Explanation

The Johnson ring counter, also known as a twisted ring counter, is a synchronous shift register with feedback from the inverted output of the last stage to the input of the first stage. This configuration generates a sequence of states that cycles through 2N unique patterns for an N-stage counter, unlike a standard ring counter which only produces N states.

Circuit Topology

The basic Johnson counter consists of:

• D flip-flops connected in series (typically 4 or more stages)
• An inverter between the Q̅ output of the last stage and the D input of the first stage
• A common clock signal driving all flip-flops
• Optional reset circuitry for initialization

State Transition Analysis

The counter progresses through states according to the following rules:

For a 4-stage counter, the complete state sequence is:

Timing Considerations

The maximum operating frequency is determined by:

where t_pd(FF) is flip-flop propagation delay, t_pd(INV) is inverter delay, and t_su is setup time. Metastability can occur if these timing constraints are violated during the feedback loop.

Practical Implementation Notes

• Power-on initialization requires either asynchronous reset or a startup circuit
• Glitches may appear during state transitions due to unequal propagation delays
• For reliable operation, clock skew between stages should be minimized
• CMOS implementations typically consume less power than TTL variants

2.3 Timing Diagram Analysis

Clock Synchronization and State Transition

The Johnson Ring Counter operates synchronously, with state transitions occurring at the rising or falling edge of the clock signal. For an n-stage counter, the timing diagram illustrates how each flip-flop (FF₀ to FF_n-1) propagates its output after a clock edge. The propagation delay (t_pd) between stages must satisfy:

where T_clk is the clock period and t_setup is the setup time of the flip-flops. Violating this condition leads to metastability or incorrect state transitions.

Waveform Interpretation

The timing diagram for a 4-stage Johnson counter (8 unique states) shows:

• Clock signal (CLK): Square wave with 50% duty cycle.
• Outputs (Q₀ to Q₃): Delayed by one clock cycle relative to the previous stage.
• Recirculation: The inverted output of the last stage (Q̄₃) feeds back into FF₀.

Critical Timing Parameters

The following parameters govern correct operation:

• Clock-to-Q Delay (t_cq): Time for a flip-flop output to stabilize after a clock edge.
• Feedback Path Delay: Must be less than T_clk to prevent race conditions.
• Maximum Clock Frequency: Derived from the slowest stage:

Practical Implications

In high-speed applications (e.g., serial-to-parallel converters), timing mismatches introduce jitter. SPICE simulations or hardware logic analyzers are used to validate the timing diagram against theoretical predictions. For fault tolerance, designers often include:

• Clock skew compensation circuits.
• Glitch suppression filters on feedback paths.

3.1 Frequency Division

A Johnson Ring Counter inherently performs frequency division due to its circulating shift-register structure. For an n-stage counter, the output frequency at any given stage is 1/(2n) of the input clock frequency. This property arises because the counter requires 2n clock cycles to complete one full cycle of its state sequence.

Mathematical Derivation

Consider an n-bit Johnson counter. The total number of unique states is 2n, as each bit propagates through the shift register and inverts upon completing the loop. The output frequency f_out is derived as follows:

where:

• f_clk is the input clock frequency,
• n is the number of stages in the counter.

Practical Implications

This frequency division is useful in applications requiring subharmonic clock generation, such as:

• Digital frequency synthesizers, where precise lower-frequency signals are needed.
• Timing circuits, where synchronized slower clock domains are derived from a master clock.
• Pulse-width modulation (PWM) controllers, where duty cycle adjustments rely on divided frequencies.

Phase-Shifted Outputs

Each stage of the Johnson counter provides a signal with a phase shift of 360°/(2n) relative to the previous stage. For example, a 4-stage counter (n=4) yields outputs with 45° phase separation, useful in polyphase signal generation.

Stability and Noise Considerations

Unlike binary counters, Johnson counters exhibit reduced glitch-related noise during state transitions, as only one bit changes at a time. This makes them advantageous in high-precision frequency division where spurious transitions must be minimized.

Real-World Example

In a 5-stage Johnson counter (n=5), a 10 MHz clock input produces a 1 MHz output (f_out = 10 MHz / (2×5) = 1 MHz). This is commonly used in decade counter applications where a clean, glitch-free division-by-10 is required.

3.2 Pattern Generation

Fundamentals of Pattern Sequencing

A Johnson ring counter, also known as a twisted ring counter, generates a deterministic sequence of states by feeding the inverted output of the last flip-flop back to the input of the first. For an n-stage counter, this produces 2n unique states, unlike a standard ring counter’s n states. The pattern evolves as a walking ring of alternating 1s and 0s, with a Hamming distance of 1 between consecutive states.

State Transition Analysis

Consider a 4-bit Johnson counter initialized to 0000. The sequence progresses as follows:

After reaching 1111, the sequence mirrors backward (0111 → 0011 → ...), forming a closed loop. The state transition graph is a Hamiltonian cycle through all possible 2n configurations.

Applications in Control Systems

Johnson counters are favored in:

• Phase-shift generation for multi-phase clock signals in power electronics.
• Mechanical position encoders, where Gray-code-like properties minimize read errors.
• Test pattern generation for built-in self-test (BIST) circuits due to predictable transitions.

Case Study: Stepper Motor Control

A 4-bit Johnson counter driving an H-bridge produces the sequence 1000 → 1100 → 0100 → 0110 → ..., enabling full-step control of a bipolar stepper motor with minimal glitch power dissipation.

Mathematical Derivation of Sequence Length

The number of unique states L for an n-stage counter is derived from the recurrence relation:

This contrasts with a linear feedback shift register (LFSR), where L = 2ⁿ − 1. The reduced state space simplifies decoding logic in applications like rotary switch debouncing.

Johnson Ring Counter

Structure and Operation

A Johnson ring counter, also known as a twisted ring counter, is a modified shift register where the inverted output of the last stage is fed back to the input of the first stage. This feedback mechanism creates a unique sequence of states that cycles through 2N distinct patterns for an N-stage counter, unlike a standard ring counter which cycles through only N states.

The basic structure consists of D-type flip-flops connected in series, with the Q' (complementary output) of the final stage driving the D input of the first stage. For a 4-stage Johnson counter, the state transition sequence is:

Mathematical Analysis

The maximum count length L of an N-bit Johnson counter is given by:

Propagation delay (t_p) is critical for high-speed operation. For a cascade of N flip-flops with individual delay t_ff:

Applications

• Phase generators in clock distribution networks, producing non-overlapping signals.
• Sequence detectors in communication protocols, leveraging its predictable state transitions.
• Control logic for stepper motors, where the cyclic output drives coil activation.

Design Considerations

To initialize the counter, a reset circuit forces all flip-flops to a known state (typically all zeros). Metastability risks arise if the feedback loop violates setup/hold times, necessitating:

where t_clk is the clock period and t_setup is the flip-flop setup time.

Power Consumption

Dynamic power dissipation scales quadratically with clock frequency (f) due to capacitive charging:

where C_eff is the effective switched capacitance per stage.

4.1 Key Benefits

High Noise Immunity and Robustness

The Johnson Ring Counter exhibits superior noise immunity compared to standard binary counters due to its use of a closed-loop shift register. Since only one bit changes state at a time (unlike binary counters where multiple bits may toggle simultaneously), the counter is less susceptible to transient noise and glitches. This makes it ideal for high-reliability applications such as industrial automation and aerospace systems.

Simplified Decoding Logic

A Johnson counter with n flip-flops produces 2n distinct states, allowing straightforward decoding without complex combinational logic. The output sequence follows a predictable pattern (e.g., 0000 → 1000 → 1100 → 1110 → 1111 → 0111 → 0011 → 0001 → 0000), enabling efficient state detection using minimal AND gates. This reduces propagation delays and power consumption in finite-state machine designs.

Self-Correcting Property

Unlike conventional ring counters, the Johnson configuration inherently corrects invalid states due to its feedback mechanism. If the counter enters an erroneous state (e.g., from a power glitch), it automatically returns to a valid state within n clock cycles. This eliminates the need for external reset circuitry in mission-critical systems.

Low Power Consumption

The single-bit transition property minimizes dynamic power dissipation, governed by:

where α (activity factor) is significantly lower than in binary counters. This advantage is critical for battery-operated and IoT devices.

Phase Generation and Clock Division

The Johnson counter naturally generates 2n non-overlapping phases, useful in multi-phase clock systems. For example, a 4-stage counter divides the input clock by 8 while providing eight 45°-spaced phases, simplifying quadrature modulation/demodulation in RF systems.

Applications in High-Speed Systems

The absence of combinational logic between stages allows operation at higher frequencies than synchronous binary counters. This is exploited in:

• Optical encoders for precision positioning
• Time-to-digital converters (TDCs) in particle physics experiments
• Spread-spectrum clock generation

4.2 Common Challenges and Solutions

Race Conditions and Timing Hazards

Johnson ring counters rely on synchronous clocking to ensure proper state transitions. However, propagation delays in flip-flops can lead to race conditions, where intermediate states are incorrectly sampled. The worst-case scenario occurs when the delay between stages (t_pd) approaches half the clock period (T_clk/2). To mitigate this:

Where t_setup is the setup time of the flip-flops. For high-frequency operation, use edge-triggered flip-flops with low propagation delay (e.g., 74HC74 for TTL logic).

Power-On Reset (POR) Issues

Without a reset mechanism, the counter may initialize to an invalid state (e.g., 0101). Solutions include:

• Asynchronous reset: Tie all flip-flop reset pins to a common RC circuit (time constant ≥ 5× clock period).
• Synchronous preset: Load a valid state (e.g., 0001) using a startup pulse synchronized to the clock.

Glitches in Decoding Logic

When deriving outputs from intermediate flip-flop states, combinatorial logic may produce transient glitches. For a 4-stage counter, the hazard-free decoding equation for state S_n is:

Implement this with 2-input AND gates where one input is inverted. For higher noise immunity, add Schmitt triggers or pipeline the outputs.

Clock Skew Management

Uneven clock distribution causes stage-to-stage skew, degrading maximum operating frequency. To minimize skew:

• Use a balanced clock tree with equal trace lengths.
• Insert buffer ICs (e.g., 74HC125) for fanout > 4.
• Measure skew with an oscilloscope; keep it below 10% of T_clk.

Metastability in Feedback Path

The inverted feedback from the last stage creates a potential metastability point. The probability of metastability (P_meta) is:

Where t_r is the reset time constant and τ is the flip-flop's metastability resolution time. Use flip-flops with built-in metastability hardening (e.g., 74FXX series) for critical applications.

EMI and Power Supply Noise

High-speed toggling generates broadband EMI. Countermeasures include:

• Place 100nF decoupling capacitors within 5mm of each IC.
• Use twisted-pair wiring for clock signals.
• Implement spread-spectrum clocking if jitter is tolerable.

Thermal Effects on Propagation Delay

For every 10°C rise in temperature, CMOS propagation delay increases by ~3%. In precision timing applications:

• Derate the maximum clock frequency by 20% for industrial temperature ranges.
• Use thermally compensated oscillators (TCXO) for clock generation.

5.1 Recommended Books

• DIGITAL ELECTRONICS: CIRCUITS AND SYSTEMS - ResearchGate — Ring Counter 131 . xiii . 5.11.2. Johnson Counter 132 . 5.11.3. Decade Counter 133 . Summary 135 . Review Questions 137 . Solved Problems 137 . Exercise 138 . ... Reviews the book, Psychological ...
• Practical Electronics for Inventors, Fourth Edition PDF - Zoboko.com — Chapter 469: 12.8.4 Ring Counter (Shift Register Sequencer) Chapter 470: 12.8.5 Johnson Shift Counter; Chapter 471: 12.8.6 Shift Register ICs; Chapter 472: 12.8.7 Simple Shift Register Applications; Chapter 473: 12.9 Analog/Digital Interfacing; Chapter 474: 12.9.1 Triggering Simple Logic Responses from Analog Signals
• (PDF) Hand Book of Electronics - ResearchGate — 10.7.3 Thermal Noise or Johnson Noise . 10.7.4 Shot noise . 10.7.5 Noise Figure . ... 31.9.2 Johnson Counter or Twisted Ring Counter . 31.10 Shift Register IC . D. ... Electronic Book: Hand and ...
• Digital Electronic - Flip eBook Pages 1-50 | AnyFlip — 6.4 Shift Register Counter 110 6.4.1 Ring Counter 6.4.2 Johnson Counter Exercise 6 References DIGITAL ELECTRONIC NUMBER AND CODE SYSTEMS CHAPTER 1 NUMBER AND CODE SYSTEMS OUTCOMES: Upon completion of this topic, students should be able to: 1. illustrate the knowledge of digital number systems: decimal, binary, octal and
• Analog & Digital Electronics DOTE Text Book | PDF | Operational ... — Analog & Digital Electronics DOTE Text Book - Free download as PDF File (.pdf), Text File (.txt) or read online for free. ... Mod n counter - Up Down IV Counter - Preset table counter - Ring counter - Johnson counter - 71 - 93 Synchronous counter - State diagram ... octal 1 5 1.. 6 4. Convert Hexa-decimal numberA26.F4 to its equivalent binary ...
• VHDL Code For 4-Bit Ring Counter and Johnson Counter — The document describes VHDL code for 4-bit ring and Johnson counters. It provides code for a ring counter that shifts a 1 through the flip flops on each clock cycle. A Johnson counter is also described which is similar to a ring counter but inverts the output of the last flip flop before feeding it back to the first flip flop. Testbenches are included to simulate and observe the output ...
• PDF FOUNDATIONS OF DIGITAL ELECTRONICS - University of Nairobi — 1.2 Unsigned binary arithmetic 5 1.3 Signed binary arithmetic 7 1.4 The octal number system 13 ... the Johnson shift register counter and the ring shift registers counter are discussed. A discussion of the use of shift registers in arithmetic circuits and in the ... recommended books for further reading is given in the bibliography.
• Digital VLSI Design and Simulation with Verilog : Frontmatter — Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content ... 2.3.3 Design of a 3-Bit Synchronous Up-counter 34 2.3.4 Ring Counter 36 2.3.5 Johnson Counter 37 2.4 Finite State Machine (FSM) 37
• ADE Module - 5-1 - IT IS NOTES - Module - Studocu — Fig.5: 4-bit Ring counter Using preset and clear input initial value of the output is defined. The first flipflop output is set to logic 1 and all other flipflop output is set to logic 0. The initial status of the D flip-flops in the absence of clock signal is 1000. This status repeats for every four negative edge transitions of clock signal.
• PDF 1 Title page - ResearchGate — The book has been systematically organized and present form help the students to understand the fundamentals of digital electronics. I am deeply indebted to Prof. P. J. George, Chairman, Depatment ...

5.2 Research Papers and Articles

• 12 bit 3.072 GS/s 32‐way time‐interleaved pipelined ADC with digital ... — 3.1.1 Johnson counter. The Johnson counter is a type of ring counter, also known as the twisted ring counter . However, in contrast to a traditional ring counter, instead of Q, the complement of the output Q′ is sent to the input of the first DFF. Thus, in the Johnson counter, the output of the first DFF changes its state after every 2N cycles.
• DIGITAL ELECTRONICS: CIRCUITS AND SYSTEMS - ResearchGate — Ring Counter 131 . xiii . 5.11.2. Johnson Counter 132 . 5.11.3. Decade Counter 133 . Summary 135 . Review Questions 137 . ... Both the papers and the commentaries are uneven in quality, and there ...
• PDF Registers and counters - Springer — states and is known as a mod-n or divide-by-n ring counter. A divide­ by-4 ring counter and associated waveforms are shown in Fig. 5.4. A more efficient use of the register as a counter can be achieved by inverting the signal between the serial output and the serial input. This produces a twisted or switch-tail ring counter; a circuit and ...
• 4-bit Johnson Counter with Ring Oscillator using SKY130nm PDK — A Johnson counter is also known as a k‐bit switch‐tail ring counter with 2k decoding gates which provides output for 2k timing signals. A k‐bit ring counter circulates a single bit among the flip‐flops and can provide k distinguishable states. To double the number of states the shift register must be connected as a switch-tail ring counter.
• PDF Chapter 5 Flip-Flops, Registers, and Counters - University of Utah — A three-bit up-counter. T Q Clock Q T Q Q T Q Q 1 Q 0 Q 1 Q 2 (a) Circuit Clock Q 0 Q 1 ... Ring counter. Please see "portrait orientation" PowerPoint file for Chapter 5 ... Johnson counter. Figure 5.30. Three types of storage elements in a schematic. Figure 5.31. Gated D latch generated by CAD tools. Data Clock
• Sequential Logic Design - SpringerLink — 5.4.7 Johnson Counters. The Johnson counter is the special type of synchronous counter and designed by using the shift register . The internal structure for three-bit Johnson counter is shown in Fig. 5.23.
• Design of Time Efficient 8-Bit Ring Counter using Pulsed Latches — This paper proposes 8-bit ring counter using pulsed latches. In recent years time efficient circuits are given utmost importance. ... International Journal of Engineering Research and Applications, 2017. This paper presents an improved low power design of a 4-bit Johnson Counter which is designed using and Clock enable method. ... In this paper ...
• PDF Design and Measurement of Parameter-Specific Ring Oscillators — appreciate the sponsors of my research: the UC Discovery Grant ele07-10283 under the IMPACT project and SRC Research Tasks 1443. I am grateful to my research group members for their friendship and support during the past years: Daniel Ceperley, Eric Chin, Chris Clifford, Marshal Miller, Wojtek Poppe, and Juliet Rubinstein.
• A test set embedding approach based on twisted-ring counter with few ... — A test set embedding approach based on twisted-ring counter with few seeds. Author links open overlay panel ... an effective 2 m-segment-reduction scheme is proposed in this paper, in which a special counter with a step ... China. His current research interests include BIST, test data compression, and IC design. Yi-zheng Ye was born in 1937 ...
• High speed optical 4-bit twisted ring counter using electro-optic ... — A 4-bit twisted ring counter is demonstrated utilizing the electro-optic effect of lithium niobate based Mach-Zehnder Interferometer (MZI). The MZI structures working on the principle of electro-optic effect show the powerful ability to switch the optical signal from one output port to the other. The theoretical description along with appropriate mathematical formulation is provided and the ...

5.3 Online Resources

• BECL305 ADE Lab Manual (1) - 1 | PDF | Electrical Network - Scribd — Understand the operation of electronic circuits and their working. ... 3 -1.875V 0100 4 -2.5V 0101 5 -3.125V 0110 6 -3.75V 0111 7 -4.375V 1000 8 -5V 1001 9 -5.625V 1010 10 -6.25V 1011 ... A Johnson counter (or switch tail ring counter, twisted-ring counter, walking-ring counter, ...
• PDF Logisim-Evolution Lab Manual - Hackaday.io — Figure 6.1 Asynchronous Up Counter 48 Figure 6.2 Asynchronous Down Counter 49 Figure 6.3 Asynchronous Decade Counter 51 Figure 6.4 Synchronous Ring Counter 53 Figure 6.5 Synchronous Johnson Counter 54 Figure 6.6 Main Circuit 55 Figure 6.7 Timing Diagram for Up Counter 56 Figure 6.8 Set Up Chronogram 57 Figure 6.9 Chronogram Ready 58 xi
• PDF Chapter 5 Flip-Flops, Registers, and Counters - University of Utah — A three-bit up-counter. T Q Clock Q T Q Q T Q Q 1 Q 0 Q 1 Q 2 (a) Circuit Clock Q 0 Q 1 ... Ring counter. Please see "portrait orientation" PowerPoint file for Chapter 5 ... Johnson counter. Figure 5.30. Three types of storage elements in a schematic. Figure 5.31. Gated D latch generated by CAD tools. Data Clock
• Digital Electronic - Flip eBook Pages 101-120 | AnyFlip — mod-2n counter. The circuit above shows a 4-bit Johnson counter. The state sequence for the counter is given in the table as well as the animation on the left. Figure 6.10 Johnson counter Table 6.8 Operation of Johnson counter Beware that for both the Ring and the Johnson counter must initially be forced into a valid state
• Logisim Labs | PDF | Logic Gate | Electronic Circuits - Scribd — Table 6.4: Ring Counter Output 54 counters. 6.2.5 Synchronous Johnson Counter. A Johnson Counter is similar to a ring counter in that a high bit value is shifted through the entire binary word. The difference is that the feedback loop comes from the Q' output of the last stage rather than the Q output.
• Counters in Digital Logic - Naukri Code 360 — No. of states in Johnson counter = No. of flip-flops used ; Number of used states = 2n; Number of unused states = 2n - 2*n; State Diagram Block Diagram of a Johnson Counter. The 4-bit Johnson counter uses four D flip flops, similar to the Ring counter, and the same clock pulse is applied to all of the flip flops' inputs. Truth Table Ripple Counter
• DLD Chapter-5.pdf - SlideShare — It describes asynchronous and synchronous counters, and different types including up/down counters, decade counters, ring counters, and Johnson counters. Examples of counter applications are given such as in kitchen appliances, washing machines, microwaves, and programmable logic controllers.
• Digital Electronic - Flip eBook Pages 1-50 | AnyFlip — 6.4 Shift Register Counter 110 6.4.1 Ring Counter 6.4.2 Johnson Counter Exercise 6 References DIGITAL ELECTRONIC NUMBER AND CODE SYSTEMS CHAPTER 1 NUMBER AND CODE SYSTEMS OUTCOMES: Upon completion of this topic, students should be able to: 1. illustrate the knowledge of digital number systems: decimal, binary, octal and
• Johnson Counter - Naukri Code 360 — A Johnson counter is a special kind of digital counter that cycles through a set of states in a loop, using a simple chain of flip-flops connected in a clever way. It's known for being easy to design and for its ability to create predictable, repeating patterns of binary values.
• PDF Introduction to Programmable Logic Devices - University of Texas at ... — Introduction to Programmable Logic Devices (Class 7.2 - 2/28/2013) CSE 2441 - Introduction to Digital Logic Spring 2013 Instructor - Bill Carroll, Professor of CSE