# Why are Mod-10 & Mod-5 decade counters while Mod-6 & Mod-8 not?

• Wrichik Basu
In summary, the book Digital Principles and Applications by Malvino, Leach and Saha does not list Mod-8, Mod-3, Mod-6 etc. as decade counters. It only lists Mod-5 and Mod-10 counters. JK flip-flops are the only type of flip-flop that can be used to make the counters. All the counters in the book use JK flip-flops.
Wrichik Basu
Gold Member
I am following the book Digital Principles and Applications by Malvino, Leach and Saha.

Under the heading "Decade Counters", the book lists only Mod-5 and Mod-10 counters. It doesn't state why these are decade counters, or what decade counters are. Others like Mod-8, Mod-3, Mod-6 etc. are listed outside that heading.

All the counters are using JK flip-flop in this book. While I know that other flip-flops can be used to make the counters, I request you to stick to JK flip-flops, because I am new to this topic and am already confused.

For reference, here is the diagram of the Mod-5 up counter given in my book (outputs are A, B and C; C is the MSB, while A is the LSB.):

and here is the Mod-8 up counter (outputs are A, B and C; C is the MSB, while A is the LSB.):

I searched Wikipedia to find out what decade counters are.
Wikipedia said:
A decade counter is one that counts in decimal digits, rather than binary.
This makes things confusing for me. How can something count in decimals? Consider the Mod-5 counter above. It goes from 000 to 100. Isn't that counting in binary rather than decimal?

Speaking the other way round, the Mod-8 counter goes from decimal 0 to 7. I can easily get the output in decimal if I decode the necessary outputs. So why is it not a decade counter?

https://www.electronics-tutorials.ws/counter/mod-counters.html says,
Decade (divide-by-10) counters such as the TTL 74LS90, have 10 states in its counting sequence making it suitable for human interfacing where a digital display is required.
According to this definition, a Mod-5 counter doesn't qualify as a decade counter because it has five states, from decimal 0 to 4.

So, why are Mod-10 and Mod-5 decade counters and Mod-6 and Mod-8 not? Or is the book incorrect? Or am I misinterpreting something?

Wrichik Basu said:
I am following the book Digital Principles and Applications by Malvino, Leach and Saha.

Under the heading "Decade Counters", the book lists only Mod-5 and Mod-10 counters. It doesn't state why these are decade counters, or what decade counters are. Others like Mod-8, Mod-3, Mod-6 etc. are listed outside that heading.

All the counters are using JK flip-flop in this book. While I know that other flip-flops can be used to make the counters, I request you to stick to JK flip-flops, because I am new to this topic and am already confused.

For reference, here is the diagram of the Mod-5 up counter given in my book (outputs are A, B and C; C is the MSB, while A is the LSB.):

View attachment 255223

and here is the Mod-8 up counter (outputs are A, B and C; C is the MSB, while A is the LSB.):

View attachment 255222

I searched Wikipedia to find out what decade counters are.

This makes things confusing for me. How can something count in decimals? Consider the Mod-5 counter above. It goes from 000 to 100. Isn't that counting in binary rather than decimal?

Speaking the other way round, the Mod-8 counter goes from decimal 0 to 7. I can easily get the output in decimal if I decode the necessary outputs. So why is it not a decade counter?

https://www.electronics-tutorials.ws/counter/mod-counters.html says,

According to this definition, a Mod-5 counter doesn't qualify as a decade counter because it has five states, from decimal 0 to 4.

So, why are Mod-10 and Mod-5 decade counters and Mod-6 and Mod-8 not? Or is the book incorrect? Or am I misinterpreting something?
I think you are using a non-standard definition of decade counter. See here

a mod-5 counter is NOT a decade counter nor is a mod 8. Only a mod-10 counter is a decade counter. See also https://www.electronics-tutorials.ws/counter/bcd-counter-circuit.html

Decade counters count to 10 (divide by 10, mod-10, etc.). That is all.

They are often related to mod-5 counters because 5 is a factor of 10. Decade counters often count to 5 twice.

Don't get caught up memorizing useless jargon, these are all just counters. If you can learn how to divide by 3, 17 , 256, or any other number, you will know all that is technically important.

sophiecentaur, Wrichik Basu and sysprog
From: https://www.electronics-tutorials.ws/counter/bcd-counter-circuit.html
The 74LS90 BCD Counter
The 74LS90 integrated circuit is basically a MOD-10 decade counter that produces a BCD output code. The 74LS90 consists of four master-slave JK flip-flops internally connected to provide a MOD-2 (count-to-2) counter and a MOD-5 (count-to-5) counter. The 74LS90 has one independent toggle JK flip-flop driven by the CLK A input and three toggle JK flip-flops that form an asynchronous counter driven by the CLK B input as shown.​
74LS90 BCD Counter
The counters four outputs are designated by the letter symbol Q with a numeric subscript equal to the binary weight of the corresponding bit in the BCD counter circuits code. So for example, QA, QB, QC and QD. The 74LS90 counting sequence is triggered on the negative going edge of the clock signal, that is when the clock signal CLK goes from logic 1 (HIGH) to logic 0 (LOW).​
The additional input pins R1 and R2 are counter “reset” pins while inputs S1 and S2 are “set” pins. When connected to logic 1, the Reset inputs R1 and R2 reset the counter back to zero, 0 (0000), and when the Set inputs S1 and S2 are connected to logic 1, they Set the counter to maximum, or 9 (1001) regardless of the actual count number or position.​
As we said before, the 74LS90 counter consists of a divide-by-2 counter and a divide-by-5 counter within the same package. Then we can use either counter to produce a divide-by-2 frequency counter only, a divide-by-5 frequency counter only or the two together to produce our desired divide-by-10 BCD counter.​
With the four flip-flops making up the divide-by-5 counter section disabled, if a clock signal is applied to input pin 14 (CLKA) and the output taken from pin 12 (QA), we can produce a standard divide-by-2 binary counter for use in frequency dividing circuits as shown.​

Asymptotic
I believe the reason why the 74xx90 was built from separate ÷2 and ÷5 counters was for flexibility.

When connected as ÷2 followed by ÷5, it produces a BCD output code.

When connected as ÷5 followed by ÷2, it divides by 10, producing a square wave with 50% duty cycle, something not available from the BCD configuration.

berkeman, phinds, Asymptotic and 1 other person
phinds said:
a mod-5 counter is NOT a decade counter nor is a mod 8. Only a mod-10 counter is a decade counter.
That clears the confusion.
DaveE said:
Don't get caught up memorizing useless jargon, these are all just counters. If you can learn how to divide by 3, 17 , 256, or any other number, you will know all that is technically important.
True, I know that, but from the perspective of the exam, I am supposed to know this. We often encounter questions asking us to draw the circuit diagram and waveform of a decade counter.

Asymptotic
Baluncore said:
When connected as ÷5 followed by ÷2, it divides by 10, producing a square wave with 50% duty cycle, something not available from the BCD configuration.
The following binary ripple decade counter also does that:

When the count reaches 9 (=B'1001'), both inputs to the 74LS10 NAND gate are 1s, so on the next clock pulse, all 4 flip-flops go to Q=0, and the count is thus truncated, and restarts from 0 (=B'0000').

That circuit could be modified to be a 5 counter by connecting the top input of the NAND gate to ##\text Q_\text B## instead of ##\text Q_\text A##, but then the leftmost flip-flop would be superfluous -- with the 4 flip-flops, you could do, e.g., a 12 counter, truncating at 11, by connecting that top input to ##\text Q_\text C##.

sysprog said:
The following binary ripple decade counter also does that:
So which output has the 50% duty cycle?

Baluncore said:
So which output has the 50% duty cycle?
Maybe I didn't understand what you meant. In the following chart for the outputs, each output until interruption by the truncation shows a 50%-on 50%-off square wave pulse cycle that is half the frequency of its rightward neighbor. QA is 50%-on 50%-off for 5 pulse cycles.

sysprog said:
Maybe I didn't understand what you meant.
I meant a symmetrical square wave at one tenth of the input frequency, an ideal input for a PLL detector.
The closest you have is the QC output which is high for 4 out of the ten states = 40%, not 50%.

DaveE and sysprog
DaveE said:
Don't get caught up memorizing useless jargon, these are all just counters.
Here we go again with the 'what do we call it?' question. I suggest that the first PF member to read any OP which is identifiable as one of these, should post an immediate caveat before any serious response. Often it is all that's needed to head a thread in the right direction from the start.
Scientists and, perhaps Engineers in particular can be very insular in their use of terms and that textbook could have been worded in a way that would have indicated that a Mod 5 counter can be used in a decade counter. 5 and 2 are prime factors of 10 so they are both needed for a decade counter. 8 and 6 are clearly useless.

sysprog

## 1. Why are Mod-10 and Mod-5 decade counters while Mod-6 and Mod-8 are not?

Mod-10 and Mod-5 are considered decade counters because they have 10 and 5 states respectively, making them ideal for counting in decimal and binary systems. Mod-6 and Mod-8 counters have 6 and 8 states respectively, which do not align with the decimal or binary system, making them less practical for counting purposes.

## 2. How do Mod-10 and Mod-5 decade counters work?

Mod-10 and Mod-5 counters work by using a series of flip-flops to store and change the state of the counter. Each flip-flop represents a binary digit, with the number of flip-flops determining the number of states. When the counter reaches its maximum state, it resets back to its initial state and continues counting.

## 3. Can Mod-6 and Mod-8 counters be used for counting?

While Mod-6 and Mod-8 counters are not typically used for counting in decimal or binary systems, they can still be used for other applications such as frequency division or time division. They are also commonly used in digital clocks and electronic devices to keep track of time.

## 4. What are the advantages of using Mod-10 and Mod-5 decade counters?

The main advantage of using Mod-10 and Mod-5 counters is their ability to easily count in decimal and binary systems, making them useful for a variety of applications. They also have a simple and efficient design, making them cost-effective and reliable for use in electronic circuits.

## 5. Are there any alternatives to Mod-10 and Mod-5 counters?

Yes, there are alternative counters such as Mod-12 and Mod-16 counters which have 12 and 16 states respectively. These counters are commonly used in digital clocks and other electronic devices that require higher counting capabilities. However, they are more complex and may not be as cost-effective as Mod-10 and Mod-5 counters.

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