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# ina johnson counters three ffs are connected to form a counter, how many states are possible to count

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## Johnson Ring Counter and Synchronous Ring Counters

Electronics Tutorial about the Johnson Ring Counter and the Synchronous Walking Ring Counter constructed from Shift Registers

## Johnson Ring Counter

The Johnson Ring Counter consists of a number of counters connected together with the output fed back to the input

In this tutorial we will see that the Johnson ring counter is a type of counter created using shift registers, and in the previous Shift Register tutorial we saw that if we apply a serial data signal to the input of a Serial-in to Serial-out Shift Register, the same sequence of data will exit from the last flip flip in the register chain.

This serial movement of data through the resister occurs after a preset number of clock cycles thereby allowing the SISO register to act as a sort of time delay circuit to the original input data signal.

But what if we were to connect the output of this shift register back to its input so that the output from the last flip-flop, QD becomes the input of the first flip-flop, QA. We would then have a closed loop circuit that “recirculates” the same bit of DATA around a continuous loop for every state of its sequence, and this is the principal operation of a Ring Counter.

Then by looping the output back to the input, (feedback) we can convert a standard shift register circuit into a ring counter. Consider the circuit below.

### 4-bit Ring Counter

The synchronous Ring Counter example above, is preset so that exactly one data bit in the register is set to logic “1” with all the other bits reset to “0”. To achieve this, a “CLEAR” signal is firstly applied to all the flip-flops together in order to “RESET” their outputs to a logic “0” level and then a “PRESET” pulse is applied to the input of the first flip-flop ( FFA ) before the clock pulses are applied. This then places a single logic “1” value into the circuit of the ring counter.

So on each successive clock pulse, the counter circulates the same data bit between the four flip-flops over and over again around the “ring” every fourth clock cycle. But in order to cycle the data correctly around the counter we must first “load” the counter with a suitable data pattern as all logic “0’s” or all logic “1’s” outputted at each clock cycle would make the ring counter invalid.

This type of data movement is called “rotation”, and like the previous shift register, the effect of the movement of the data bit from left to right through a ring counter can be presented graphically as follows along with its timing diagram:

### Rotational Movement of a Ring Counter

Since the ring counter example shown above has four distinct states, it is also known as a “modulo-4” or “mod-4” counter with each flip-flop output having a frequency value equal to one-fourth or a quarter (1/4) that of the main clock frequency.

The “MODULO” or “MODULUS” of a counter is the number of states the counter counts or sequences through before repeating itself and a ring counter can be made to output any modulo number. A “mod-n” ring counter will require “n” number of flip-flops connected together to circulate a single data bit providing “n” different output states.

For example, a mod-8 ring counter requires eight flip-flops and a mod-16 ring counter would require sixteen flip-flops. However, as in our example above, only four of the possible sixteen states are used, making ring counters very inefficient in terms of their output state usage.

## Johnson Ring Counter

The Johnson Ring Counter or “Twisted Ring Counters”, is another shift register with feedback exactly the same as the standard Ring Counter above, except that this time the inverted output Q of the last flip-flop is now connected back to the input D of the first flip-flop as shown below.

The main advantage of this type of ring counter is that it only needs half the number of flip-flops compared to the standard ring counter then its modulo number is halved. So a “n-stage” Johnson counter will circulate a single data bit giving sequence of 2n different states and can therefore be considered as a “mod-2n counter”.

### 4-bit Johnson Ring Counter

This inversion of Q before it is fed back to input D causes the counter to “count” in a different way. Instead of counting through a fixed set of patterns like the normal ring counter such as for a 4-bit counter, “0001”(1), “0010”(2), “0100”(4), “1000”(8) and repeat, the Johnson counter counts up and then down as the initial logic “1” passes through it to the right replacing the preceding logic “0”.

A 4-bit Johnson ring counter passes blocks of four logic “0” and then four logic “1” thereby producing an 8-bit pattern. As the inverted output Q is connected to the input D this 8-bit pattern continually repeats. For example, “1000”, “1100”, “1110”, “1111”, “0111”, “0011”, “0001”, “0000” and this is demonstrated in the following table below.

स्रोत : www.electronics-tutorials.ws

## [Solved] In a Johnson's counter, all the negative triggered J

Concept: Johnson Counter: The Johnson counter is similar to the Ring counter. The only difference between the Johnson counter and the ring counter is that

Home Digital Electronics Sequential Circuits Shift Register Counters Johnson Counter

## In a Johnson's counter, all the negative triggered J-K flip-flops are used. Initially all the flip-flops are in reset condition and the outputs are Q3Q2Q1Q0 = 0000. What are the outputs of the flip-flops after the fifth negative going pulse?

This question was previously asked in

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Q3Q2Q1Q0 = 0101 Q3Q2Q1Q0 = 1000 Q3Q2Q1Q0 = 0010 Q3Q2Q1Q0 = 1110

Option 4 : Q3Q2Q1Q0 = 1110

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## Detailed Solution

Concept:Johnson Counter:

The Johnson counter is similar to the Ring counter.

The only difference between the Johnson counter and the ring counter is that the outcome of the last flip flop is passed to the first flip flop as an input.

But in the Johnson counter, the inverted outcome Q' of the last flip flop is passed as an input.

The remaining work of the Johnson counter is the same as a ring counter.

The Johnson counter is also referred to as the Creeping counter.

JK flip flop:

The JK flip flop is basically a gated SR flip-flop with the addition of a clock input circuitry that prevents the illegal or invalid output condition that can occur when both inputs S and R are equal to logic level “1”.

Due to this additional clocked input, a JK flip-flop has four possible input combinations, “logic 1”, “logic 0”, “no change” and “toggle”.

Truth Table:

Input Output Description J K Q 0 0 0 Memory no change 0 1 0 Set Q » 1 1 0 1 reset Q » 0 1 1 0 Toggle

Solution:

Q0 Q1 Q2 Q3 0 0 0 0 0 1 0 0 0 1 2 0 0 1 1 3 0 1 1 1 4 1 1 1 1 5 1 1 1 0

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Last updated on Nov 25, 2022

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## More Shift Register Counters Questions

Q1. If the following counter is initially at 0000 state then after 6th clock ABCD will be -Q2. Depending on the counter, there are up to _________ modes available on high-speed counters.Q3. If the registers have both shifts and parallel load capabilities, they are referred as _________.Q4. A five-bit asynchronous counter is shown in the figure. If the clock input frequency is 22⋅4 MHz, what is the frequency at the output E?Q5. Each flip-flop in a 4-bit ripple counter introduces a maximum delay of 40 n sec. The maximum clock frequency isQ6. In a Johnson's counter, all the negative triggered J-K flip-flops are used. Initially all the flip-flops are in reset condition and the outputs are Q3Q2Q1Q0 = 0000. What are the outputs of the flip-flops after the fifth negative going pulse?Q7. SAP-I has _______ T states, period during which register contents changeQ8. A Shift register in which the output of the last flip-flop is connected to the input of the first flip-flopQ9. An eight-bit binary ripple UP counter with a modulus of 256 is holding the count 01111111. What will be the count after 135 clock pulses?Q10. The highest speed counter is

## More Sequential Circuits Questions

Q1. Which statement is true for Mealy type Sequence Detector?Q2. Which of the following is true in case of Mealy machine?Q3. If the 5-bit ripple counter and 5-bit synchronous counter are having flip-flops with a propagation delay of 20 ns, the maximum delay in the ripple counter (x) and synchronous counter (y) will be:

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## n

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## n-bit Johnson Counter in Digital Logic

Difficulty Level : Medium

Last Updated : 16 Sep, 2021

Prerequisite – Counters

Johnson counter also known as creeping counter, is an example of synchronous counter. In Johnson counter, the complemented output of last flip flop is connected to input of first flip flop and to implement n-bit Johnson counter we require n flip-flop.It is one of the most important type of shift register counter. It is formed by the feedback of the output to its own input.Johnson counter is a ring with an inversion.Another name of Johnson counter are:creeping counter, twisted ring counter, walking counter, mobile counter and switch tail counter.

Total number of used and unused states in n-bit Johnson counter:

number of used states=2n

number of unused states=2n – 2*n

Example:

If n=4

4-bit Johnson counter

Initially, suppose all flip-flops are reset.

Truth Table:

where,

CP is clock pulse and

Q1, Q2, Q3, Q4 are the states.

Question: Determine the total number of used and unused states in 4-bit Johnson counter.

Answer: Total number of used states= 2*n

= 2*4 = 8

Total number of unused states= 2n – 2*n

= 24-2*4 = 8

The Johnson counter has same number of flip flop but it can count twice the number of states the ring counter can count.

It can be implemented using D and JK flip flop.

Johnson ring counter is used to count the data in a continuous loop.

Johnson counter is a self-decoding circuit.

Johnson counter doesn’t count in a binary sequence.

In Johnson counter more number of states remain unutilized than the number of states being utilized.

The number of flip flops needed is one half the number of timing signals.

It can be constructed for any number of timing sequence.

Applications of Johnson counter:

Johnson counter is used as a synchronous decade counter or divider circuit.

It is used in hardware logic design to create complicated Finite states machine. ex: ASIC and FPGA design.

The 3 stage Johnson counter is used as a 3 phase square wave generator which produces 1200 phase shift.

It is used to divide the frequency of the clock signal by varying their feedback.

स्रोत : www.geeksforgeeks.org

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Mohammed 2 month ago

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