What Is The Least Number Of Flip Flops That Can Be Used For A Seven Segment Display State Register
This is our complete and definitive guide to digital counters and all their types. In add-on to learning about counters, we are going to understand the difference between upward-counters and down-counters.
There's just one actually. At least just one that matters. An up-counter counts events in increasing guild. A downwards-counter counts stuff in the decreasing order. An up-downward counter is a combination of an up-counter and a downwards-counter. It tin can count in both directions, increasing every bit well equally decreasing.
Depending on the type of clock inputs, counters are of ii types: asynchronous counters and synchronous counters. We volition take a look at all the types of counters and their circuits in particular below.
What are counters?
Counters are sequential logic circuits that, in digital electronics, are used to count the number of times an event or instance takes identify.
A counter is made by cascading a series of flip-flops. Equally we know, flip-flops have a clock input. Depending on the blazon of clock input, counters are of 2 types
- Asynchronous or ripple counters.
- Synchronous counters.
Since counters kind of depend on clocks like all sequential circuits, to sympathize their working, nosotros will consider every clock cycle. Meaning, there will be changes in the states of some flip flops at every clock interval. We will try to understand the working in each clock cycle.
Based on the way the counters are used, here are the diverse types of counters:
- Up counters
- Down counters
- Up-downwardly counters
- Decade counter
- Ring counter
- Johnson counter
What is a Modernistic n counter?
Mod n or Modulus of due north, is a way of referring to the maximum count of a counter. Every counter has a limit with regards to the number they can count up or down to. Modernistic n expresses that limit.
It is an important characterization for a counter because it gives us the maximum count of the counter, too equally the number of flip-flops nowadays in the counter.
A mod n counter tin count upward to north events. We tin can mathematically represent a mod n counter as
n = 
due north = modulus/maximum event count of the counter. This is the number of states that the counter has.
North = Number of flip-flops connected in cascade
– i = Maximum decimal count it can achieve. Because binary numbers start counting from 0, so for a counter that can count up to 4 events, its decimal equivalent volition exist 3 only (0,1,2,3). Example: Modernistic 8 counter
Modernistic eight ways n = 8. From the equation in a higher place
8 =
Thus, N = iii.
Which means that this is a counter with iii flip-flops, which ways three $.25, having viii stable states (000 to 111) and capable of counting eight events or up to the decimal number
What is a synchronous counter?
In a synchronous counter, all the flip-flops are synchronized to the same clock input. This means that for every clock pulse, all the flip-flops will generate an output. Since the clocking is washed in a parallel mode, synchronous counters are also known every bit parallel counters/simultaneous counters.
We can utilise JK flip-flop, D flip-flop or T flip-flops to make synchronous counters. In this post, we will be using the D flip-bomb to design our counters. The methodology for designing the counters with other flip-flops varies with the type of flip-flops.
What are up counters, down counters and up-down counters?
Well as their names imply, up counters count upwards or incrementally. Downwards counters count downwards or in a decremental mode. Up-down counters can count both upwards also as downwardly.
How to design a 2-scrap synchronous upward counter?
Step 1: Find the number of flip-flops and choose the type of flip-flop.
Since this is a two-bit synchronous counter, we can deduce the following. There will exist 2 flip-flops. These flip-flops volition have the same RST signal and the same CLK signal. We will be using the D flip-flop to pattern this counter.
Step 2: Go along co-ordinate to the flip-flop called.
Since we are using the D flip-flop, the next pace is to draw the truth table for the counter.
The counting should start from i and reset to 0 in the end. So the display would start with displaying 1, 2, 3 so 0.
Truth table for the 2-bit synchronous upward counter
Here's what the truth table will look like. Q represents the previous output, and Qn represents the current output.
| Q1 | Q0 | Qn1 | Qn0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 1 |
| one | ane | 0 | 0 |
Another handy tip for designing synchronous counters using D flip-flop is that for the 1st flip-flop, you have to connect the inverted output to the input direct. You don't have to perform any extra logical functioning.
So, in this example, we will summate the equation for only Qn1 to be fed back to Q1. From the truth table, using the shortcut we saw in our mail on digital comparators, we get the following.
Qn1 is loftier when Q1 is low AND Q0 is high, OR Q1 is high AND Q0 is low. This gives us the post-obit equation
Qn1 = 
The resulting excursion for the 2-fleck synchronous up counter is as shown beneath.
How to pattern a two-bit synchronous down counter?
Step 1: Discover the number of flip-flops and choose the type of flip-flop.
Since this is a 2-bit synchronous counter, we take ii flip-flops. These flip-flops volition have the same RST signal and the same CLK signal. We will be using the D flip-flop to blueprint this counter.
Stride 2: Go along according to the flip-flop chosen.
Nosotros volition now design the truth table for this counter. The counter should follow the sequence 0, three, 2, 1, 0, three, 2, 1.
Truth tabular array for the two-flake synchronous downwards counter
| Q1 | Q0 | Qn1 | Qn0 |
| 0 | 0 | 0 | 0 |
| 0 | 1 | one | one |
| i | 0 | ane | 0 |
| 1 | ane | 0 | 1 |
Hence, we can run across that the equation that we will derive for Qn1 is the same as that for the upwardly counter. The only difference in the construction will be that in the two-bit synchronous down counter, the output will be taken from the inverted outputs of the flip-bomb.
How to design a 3-scrap synchronous up counter?
We will need three flip-flops. These three flip-flops are synchronous to the same clock input. They will have the same reset bespeak as well. Since nosotros are using the D flip-flop to construct this, we can straightaway pattern the truth table.
The sequence will be 1, two, three, 4, five, 6, 7, 0.
| Q2 | Q1 | Q0 | Qn2 | Qn1 | Qn0 |
| 0 | 0 | 0 | 0 | 0 | i |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | one | 1 | 0 |
| ane | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 |
Nosotros accept our shortcut of connecting Qn0 to Q0 straight. For the inputs of the remaining two flip-flops, we volition solve the truth table using Thou-maps to derive the equations.
Thus Qn1 =
And Qn2 = 
Implementing the logic equations above , we get the following circuit for a 3-scrap synchronous up counter.
How to design a 3-flake synchronous down counter?
The circuit diagram for the iii-chip synchronous downward counter is the same as that of the upward counter. The merely difference is that instead of attaching the non-inverted outputs to the display port, we will attach the inverted outputs.
How to design a 3-bit synchronous up-down counter?
An up-down counter is capable of counting in both incremental and decremental style. For a iii-bit synchronous upwards-downward counter, we need three flip-flops, with the aforementioned clock and reset inputs.
The style to accomplish the ability to count in both the directions is by combining the designs for the up and the down counters and using a switch to alternate between them.
We know that for the upwards and downwardly counters, the pattern of the excursion is the same. The only difference is that for the up counter the output is taken at the non-inverting output ports of the flip-flops. Whereas, for the down counter, the output is taken at the inverting output ports of the flip-flops.
So nosotros take a total of 3+3 outputs. When nosotros combine them, we become six outputs, and now we need one switch input.
From our post on multiplexers, we know that we tin use three ii:1 multiplexers connected via their select lines. This would give u.s. six inputs, one select line, and iii outputs.
Perfect. That is exactly what we demand.
Certain, we tin't expect your listen to jump straightaway to multiplexers. But remember that multiplexers give you an option of choosing between multiple inputs. And so information technology does an fantabulous chore of being a switch in digital electronics.
The resulting circuit diagram of the up-downwardly counter is shown below.
How to pattern a four-bit synchronous up counter?
Since this is a 4-bit synchronous up counter, nosotros will need four flip-flops. These flip-flops will take the same RST signal and the aforementioned CLK bespeak. Nosotros will exist using the D flip-flop to design this counter.
We will beginning right away with the design of the truth tabular array for this counter. The 4-fleck synchronous up counter should follow the sequence ane, 2, 3, 4, 5, 6, vii, eight, 9, 10, 11, 12, 13, 14, 15, 0.
| Q3 | Q2 | Q1 | Q0 | Qn3 | Qn2 | Qn1 | Qn0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | ane |
| 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | i | i |
| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 0 | ane | 0 | 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 | 1 | ane | 0 |
| 0 | i | 1 | 0 | 0 | 1 | i | 1 |
| 0 | 1 | ane | 1 | 1 | 0 | 0 | 0 |
| one | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | ane | 0 | i | 0 | 1 | i |
| 1 | 0 | ane | one | one | 1 | 0 | 0 |
| 1 | ane | 0 | 0 | 1 | 1 | 0 | 1 |
| i | 1 | 0 | ane | one | ane | 1 | 0 |
| 1 | 1 | 1 | 0 | one | ane | 1 | 1 |
| 1 | 1 | i | 1 | 0 | 0 | 0 | 0 |
The input to the outset flip-flop D0 volition come straight from its ain inverted output. Nosotros will apply Kmaps to notice the logic equations for the remaining flip-flops.
Hence the input to the 4th flip-flop volition accept the post-obit logic expression
Therefore from the Kmap, the input equation for the third flip-flop is
And the equation for the for the 2d flip-flop is
From the above equations, we obtain the logic excursion for the iv-fleck synchronous upwards counter below.
How to design a 4-scrap synchronous down counter and iv-bit synchronous up-down counter?
For the iv-bit synchronous down counter, just connect the inverted outputs of the flip-flops to the display in the excursion diagram of the up-counter shown higher up. Whereas for the up-down counter, you tin can utilize multiplexers every bit switches as we saw in the blueprint of the three-scrap synchronous up-downwardly counter.
What is an asynchronous counter?
In an asynchronous counter, all the clock inputs of the flip-flops have a unique input that is not shared with any other flip-flop in the system.
In fact, in an asynchronous counter, only the first flip-flop is given a clock (CLK) input. The output of the kickoff flip-flop is then connected to the clock input of the subsequent flip-flop and and then on.
Now, think nigh the output for a 2nd. A flip-flop is activated when information technology receives a clock pulse. Then the 2d flip-flop and all the subsequent flip-flops in an asynchronous counter get active when their preceding flip-bomb gives an output.
Thus, the clock passes as a ripple through the cascade of flip-flops. Hence, asynchronous counters are alternatively also known as ripple counters .
What is the departure between a synchronous counter and an asynchronous counter?
| Synchronous Counters | Asynchronous Counters |
| All flip-flops are given the same clock simultaneously | The flip-flops are not given the same clock |
| In that location is no connection betwixt the output of a flip-flop and the clock input of the side by side flip-bomb. | The output of a flip-bomb is given as the clock input to the next flip-flop |
| The settling time is equal to the fourth dimension it takes for the final flip-flop to become activated. This is quite less compared to the asynchronous counters. | The settling time or the time taken for all the flip-flops to go activated is equal to the sum of all the times needed to actuate the last flip-flop. |
| Information technology is known equally a parallel counter | It is known as a serial counter |
| This design gets more complicated as the number of flip-flops increases | The design of asynchronous counters is easy |
| Synchronous counters are faster | Asynchronous counters are slower |
A handy tip for designing asynchronous counters
When you are designing asynchronous counters using D flip-flops, all the inputs of the flip-flops are continued to their ain inverted outputs. The only divergence betwixt an upwards-counter and a down counter stems from the ports that are continued to the display.
For up-counters, the not-inverted output, Q, is connected to the display. Whereas for a downwards counter, the inverted output, nQ, is connected to the brandish.
How to design a 4-flake asynchronous up counter?
This is an easy circuit to blueprint. We know we are going to have 4 flip-flops. Merely the showtime flip-bomb is going to have a clock input. The clock inputs of the remaining flip-flops have the outputs of their preceding flip-flops equally inputs.
Finally, the non-inverted outputs of the flip-flops will connect to the brandish in the order of which flip-flop gets the first clock input.
So LSB will be the flip-flop that gets the start clock input. And MSB volition be the flip-bomb which gets the clock input in the end. The resulting circuit for a four-bit asynchronous upward counter is shown below.
How to design a 4-bit asynchronous downwards counter?
We mentioned above that to blueprint a downwardly-counter, there is only one change that you demand to contain. And that change to the up-counter'southward circuit is to take the output from the inverted output ports of the flip-flops. And that is true.
Notwithstanding, there is one other thing that you tin can practise.
Instead of providing the output from the inverted ports, you tin can stick with the non-inverted ports. Just instead of taking the clock output from Q, take information technology from nQ. And you lot will become your four-scrap asynchronous down counter down-counter.
How to design a 4-bit asynchronous up-down counter?
The design remains the same. Depending on where y'all have the clock input from, your output ports for the upwardly-counting and down-counting will differ. Either way, each flip-flop will connect to a two:1 multiplexer. With the inverted and non-inverted outputs being inputs to the multiplexer.
The multiplexers are cascaded together past connecting their select inputs together. (Learn how to cascade and bring together multiplexers).
Nosotros just need one select line because there are simply two states to choose from. Depending on the value of the select pivot, the iv-fleck asynchronous upwardly-down counter's circuit tin now act as both, an up-counter and equally a downwardly-counter.
How to design a decade counter?
A decade counter counts x events or till the number 10 and so resets to zero. Recollect that reset pivot nosotros used in all of our counters above. Now it's going to come in handy. In fact, using the logic we apply to design the decade counter, you tin blueprint a counter that tin can count to any desired number that y'all wish.
A count till ten won't be possible in a 3-bit counter. Because 
The reset pins function is to articulate the inputs of all the flip-flops. And so nosotros need to find a mode for this circuit to count upward to 10 and then reset to 10. At the count of 10, flip-flops 1 and three will be high. Up to 10, this is the first time that this configuration will occur. But recall that we are counting 0 too, so to count ten events, we need to actually count upwardly to 9 and not 10. At the count of nine,
0 – 0000
1 – 0001
2 – 0010
3 – 0011
four – 0100
v – 0101
half-dozen – 0110
seven – 0111
8 – g
9 – 1001
10 – 1010
If we take the outputs from the MSB and LSB flip-flops and connect them to an AND gate, we tin become a logic 1 at the count of 9. If we connect the output of this AND gate to the reset pin, then nosotros can reset the flip-flops at the tenth count. This will requite us the decade counter.
Here's what the last logic circuit for the decade counter volition await like.
How to pattern a ring counter?
Just as its proper noun suggests, a ring counter has ane of its outputs connect back to the input. It is thus making a band. Band counters are serial shift registers that human action as counters. There are 2 types of ring counters.
- Directly band counter – The not-inverting output (Q) of the last flip-flop is connected to the first flip-flop.
- Johnson ring counter/Twisted ring counter – The inverting output (nQ) of the terminal flip-flop is connected to the first flip-flop.
How is a ring counter constructed?
A band counter is substantially a slightly modified parallel in series out (PISO) shift register that acts as a counter.
How? Unproblematic.
We but take outputs from each of the flip-flops and adhere them to a brandish. Here is a logic circuit of a 4-chip ring counter. Information technology has iv flip-flops, and each of them has its own clock input and a reset bespeak.
Okay now hither'southward a potentially confusing point. We have seen above that a Modern north counter has N flip-flops. Where n=
Mod means the number of states. Equally we volition see in the working of the ring counter. Information technology has the aforementioned number of states every bit the number of flip-flops in the system. And so for ring counters, a modernistic 4 ring counter means it has four flip-flops and iv states. States means the number of counts information technology can have. This volition become clearer when we understand the working of this 4-chip ring counter.
How does a ring counter piece of work?
Since its a Parallel In Serial Shift counter, we offset need to initiate information technology by giving information technology an input. Let'due south say we give 1000 equally the input. When the first clock pulse appears, the information is loaded to the ring counter. At the second clock pulse, the output of the terminal flip-bomb, 0, gets shifted to the outset flip-bomb. And the high bit of the kickoff flip-bomb moves to the 2d flip-flop. This continues and repeats itself after every Four clock cycles.
Since it takes the same number of clock cycles equally the number of flip-flops in the organisation, information technology means that a ring counter has only N states.
And hence, in the case of band counters, the number of flip-flops is equal to the number of states. Normal binary counters that we saw in a higher place had
For example, a 4-bit synchronous upwardly-counter had sixteen states. It could count 16 events or from 0-15 decimals. So we are losing a pregnant number of counts here. In one case a number is input to the band counter, it circulates the same pattern for every n clock cycles. n is the number of flip-flops connected to it.
Hence, it has a frequency of 1/n and is also known as a divide-past-n counter. Cheque out the pulse diagram and the truth table beneath to get a clearer picture of the working.
The timing diagram of a 4-bit ring counter
Notice the repeating pattern after the t3 pulse. The iv-flake ring counter repeats itself after four states/pulses/counts. (Source)
Truth table of a 4-flake ring counter
| QA | QB | QC | QD |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | i |
Note that a band counter does non count in an ordered sequence. The count here, as we can see from the truth table, is 8, four, 2,1,8,4,two,1, and and so on.
What are the advantages and disadvantages of a ring counter?
A small reward of a band counter is that it has an automatically decoded output. Withal, ring counters have a major disadvantage because they need to be initialized. A number needs to be loaded to the ring counter before the outset of the counting process. We had non seen this with any other counter yet. Another disadvantage is that just North states are present compared to the
How to design a Johnson band counter?
A Johnson ring counter is another type of band counter. The difference between a Johnson band counter and the straight ring counter is that in a Johnson ring counter, the inverted output of the last flip-bomb (nQ) is connected to the input of the kickoff flip-flop. The only difference between the straight band counter and the Johnson counter is that in the Johnson counter the inverted output of the final flip-flop (equally opposed to the non-inverted output in the straight ring counter) is connected equally the input to the starting time flip-bomb. Hither's the excursion diagram of a iv-bit Johnson counter and its truth tabular array.
Every number that exits the terminal flip-bomb will be inverted and and then given as input to the first flip-flop.
Truth tabular array of a Johnson ring counter
| Qa | Qb | Qc | Qd |
| 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | one | 0 | 0 |
| 1 | 1 | one | 0 |
| i | 1 | i | 1 |
| 0 | 1 | one | 1 |
| 0 | 0 | one | ane |
| 0 | 0 | 0 | ane |
The truth tabular array starts from 0000. This means that it is cocky-actuating.
The Johnson counter does non need any input. Moreover, a Johnson counter has more states than a directly ring counter. A binary counter has
If y'all feel like building a mini project to empathise the working of a counter practically, here'south a expert one:
If you found this post informative or would like us to add some more concepts or explain things differently, let us know down below.
What Is The Least Number Of Flip Flops That Can Be Used For A Seven Segment Display State Register,
Source: https://technobyte.org/counters-up-down-synchronous-asynchronous/
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