How can I design a synchronous counter using NAND and inverters?

[Agent]

Hey, I have some problems with my synchronous counter. Here is what I got. sorry for the big and bad quality of the pic. My scanner sucks :(

Here's the karnaugh map. I need to simplify them and use only NAND and inverters if needed.
http://img101.imageshack.us/img101/7335/hw4na.jpg

I need to design it in pspice (Schematics) along with the truth table.
http://img101.imageshack.us/img101/1461/hw21sf.jpg

Since the last two in the truth table is wrong, the whole thing is wrong. I know its probably some simple stuff but I can't figure it out. (2hrs now ) Thanks for anyone that can help. And if you want, I can upload the file for those who have pspice.

Edit: I just found 2 errors in the Karnaugh map JB, but I'm pretty sure it doesn't change much.

 

[berkeman]

Ranger posted this link earlier today in the EE forum in response to a question on Synch Counters. Does it help?

http://www.allaboutcircuits.com/vol_4/chpt_11/3.html

 

[Agent]

I understand it. The thing is I can't find that wire (or gate) that is located wrong.

 

[berkeman]

I understand it. The thing is I can't find that wire (or gate) that is located wrong.

Okay. First off, for 4-bit numbers I prefer to use hex, but you can use 11-15 instead if that is more intuitive for you now. In the future, A-F will be more intuitive in your K-map.

Second, I only see 8 K-map drawings instead of 16 (oops, I mean F :rofl: ). I see all 16 state transitions accounted for in your list, but not in the K-maps. I could be missing your design strategy, though.

Last, are the errors that you found already fixed in the K-map that you posted the link to? I'll take a more detailed look if you think the linked K-map is correct and sufficient.


(EDIT -- changed my dumb typo "A-E" in 1st paragraph to "A-F")

 

[Agent]

Okay. First off, for 4-bit numbers I prefer to use hex, but you can use 11-15 instead if that is more intuitive for you now. In the future, A-E will be more intuitive in your K-map.

Second, I only see 8 K-map drawings instead of 16 (oops, I mean F :rofl: ). I see all 16 state transitions accounted for in your list, but not in the K-maps. I could be missing your design strategy, though.

Last, are the errors that you found already fixed in the K-map that you posted the link to? I'll take a more detailed look if you think the linked K-map is correct and sufficient.

The mistakes on the k-map/circuit are corrected now. Still getting the wrong answer but getting closer, I think. This is the way I learned it, just started so that's probably why. As long as I get the circuit right, I could careless which way is done. :)

 

[berkeman]

Okay, I think I see at least one error in the K-maps (I get the 8-map paradigm now, BTW). Look at JA term for square 4 -- it should be a 0, not a 1. For starting state 4, JK flop A has to hold a 0 to go to state 8. To hold a 0, JK = 0b0X, not the 0b1X that you show. Just work your way through all the K-map squares carefully, and I think you'll get it right. I know it's a bit tedious...

Here's the map transition info that I used in my initial checks (just a re-formatted version of what you have...how do I change the font to non-proportionally spaced courier or something...?)


State(decimal, hex, binary), Next State(decimal, binary):

0 0 0000 1 0001
1 1 0001 2 0010
2 2 0010 4 0100
3 3 0011 1 0001
4 4 0100 8 1000
5 5 0101 1 0001
6 6 0110 1 0001
7 7 0111 1 0001
8 8 1000 9 1001
9 9 1001 1 0001
10 A 1010 1 0001
11 B 1011 1 0001
12 C 1100 1 0001
13 D 1101 1 0001
14 E 1110 1 0001
15 F 1111 1 0001

 

[Agent]

Thanks a lot. It really helped. I'm going to continue tomorrow because like you said, it is tedious. One mistake and the whole thing goes wrong.

 

[doodle]

I did not go through the entire solution, but you made a mistake in the B flip-flop (see schematics), where you have used JB = X1X0 + 00X1 when it should have been JB = 00X1.

Here's the map transition info that I used in my initial checks (just a re-formatted version of what you have...how do I change the font to non-proportionally spaced courier or something...?)


State(decimal, hex, binary), Next State(decimal, binary):

0 0 0000 1 0001
1 1 0001 2 0010
2 2 0010 4 0100
3 3 0011 1 0001
4 4 0100 8 1000
5 5 0101 1 0001
6 6 0110 1 0001
7 7 0111 1 0001
8 8 1000 9 1001
9 9 1001 1 0001
10 A 1010 1 0001
11 B 1011 1 0001
12 C 1100 1 0001
13 D 1101 1 0001
14 E 1110 1 0001
15 F 1111 1 0001

Not exactly correct either. Sequence is 1-2-4-9-8, not 1-2-4-8-9. And for Courier-type fonts, attach the message within the keyword CODE.

 

[berkeman]

I did not go through the entire solution, but you made a mistake in the B flip-flop (see schematics), where you have used JB = X1X0 + 00X1 when it should have been JB = 00X1.



Not exactly correct either. Sequence is 1-2-4-9-8, not 1-2-4-8-9. And for Courier-type fonts, attach the message within the keyword CODE.

Ah, good point. The error I found in Agent's K-map was early though, before my state transition mistake. And thanks for the CODE tip!

 

[Agent]

Good news. I started the whole thing over. I found another mistake on the k-mart which added too extra NAND gates. I ran it and now it works out fine. Thanks for the help.

 

[goutamkundu91]

can any some one help me



Design a synchronous counter that goes through the sequence assigned to you. Any state that is not allowed should revert to the first state in the sequence at the first clock pulse.
Use the 7476 and NAND only TTL.
Use the following procedure:

1) Draw the state diagram.
2) Write the truth table.
3) Draw the excitation table for the JK flip flop.
4) Use Karnaugh Maps to simplify the logic control circuits for the flip flops.
5) Convert the logic control circuits for NAND only implementation.
6) Draw the synchronous counter using Circuit Maker and make sure it works.
7) Draw the synchronous counter using Schematics (PSpice).
8) Set up the clock for a 2 second period with 50% duty cycle.
9) Set up the simulation to run for 20 seconds.
10) Run the simulation.
11) Display the timing diagram showing the waveforms for the CLOCK, A, B, C, and D from the top down.
12) Print out the timing diagram.
13) On the schematic, change the information in the box in the lower right corner to reflect you, and print the page.
14) Write a paragraph describing how the circuit operates as it makes the transition between the third and the fourth state.

***** MUST USE SEQUENCE : 1234501

 

[goutamkundu91]

hey hi i am goutam i have the same thing to do i have sequence 1234501 , can u help me to simplfy them and use only NAND and inverters if needed , i will post the picture i need to solve the karnaugh map
[URL]http://img230.imageshack.us/i/imag00030.jpg/[/URL]
[URL]http://img13.imageshack.us/i/imag0002s0.jpg/[/URL]
thanks... please reply