# function simplification and implementation, MMExer3.24

#### PG1995

Joined Apr 15, 2011
832
Hi

Please have a look here to see my question. The solution is here; please note that many of the given solutions have been found wrong. Please help me. Thank you.

Regards
PG

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#### Georacer

Joined Nov 25, 2009
5,182
I have never met an exercise like this before. This is no problem however. I 'll present you my line of thought and we 'll see if you can reproduce it.

For the first case of the NAND-AND circuit. We 'll examine a generic NAND-AND circuit. This is the same as drawing:

So, what that picture say: If we take the SoP expression of the function F, create its NAND circuit and remove the last inverter, we have a NAND-AND circuit of F'.

This is useful to you because you can do the opposite. In order to produce the NAND-AND circuit of a function F, you can take the SoP expression of F', draw the NAND circuit of F' and by removing the last inverter you have, presto!, the NAND-AND circuit of F.

Is that clear?

Can you do the same for the rest three cases?

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#### PG1995

Joined Apr 15, 2011
832
Hi

Regards
PG

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#### PG1995

Joined Apr 15, 2011
832
I have solved it. Thank you for giving it a look.

Regards
PG

PS: Attached is the final solution. Please have a look. Thank you.

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#### Georacer

Joined Nov 25, 2009
5,182
Purrrrfect.

It's all correct as I see it. You 're getting the hang of it.

#### PG1995

Joined Apr 15, 2011
832
Hi

Could you please have a look on the attachment and let me know if the implementation is correct? It seems correct! Thanks a lot for the help.

Regards
PG

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#### Georacer

Joined Nov 25, 2009
5,182
This answer earned the Georacer seal of approval!

#### PG1995

Joined Apr 15, 2011
832
Hi again,

I was working on a problem but then something came to my mind and I thought I better ask you. Please have a look on the attachment. As you can see I didn't six combinations, 10, 11, 12, 13, 14, 15, because they won't occur. But can I use them as Don't Care Conditions to simply the minimization. Please let me know. Thank you.

Regards
PG

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#### PG1995

Joined Apr 15, 2011
832
Hi
After my last post, I decided to go with Don't Care Conditions. Please have a look on the attachment and please check if my relations for "A", "B", etc. are correct. Thanks a lot.

This is my calculation for the required stuff:
(i) Six 4-input and one 2-input (7432) OR gates
(ii) Thirteen 2-input (7408) and four 3-input (7411) AND gates
(iii) Twenty-six NOT gates (7404)
(iv) Seven 150 Ohm resistors for display unit

Is my calculation almost correct?

I don't know the number of IC for 4-input OR gates. This is one I found after googling 4072 but don't know if it's easily available. Please let me know.

Which batteries should I use? 9V battery?

You see in this video four buttons are used to input the numbers. Are these simply referred to as 'push-buttons'? And can some kind of numeric keypad (0-9) be used instead? I don't think it would be easily available on electronics shop.

Best wishes
PG

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#### Georacer

Joined Nov 25, 2009
5,182
The truth tables are all correct.

B function can be reduced to w+x'+y'z'+yz
C function can be reduced to w+x+y'+z
You forgot to group the minterm 5 for D
G function can be reduced to w+xy'+yz'+x'y

It takes some practice to notice the bigger groups.

You need only 4 inverters at max. You can create the inverted signals for the 4 inputs and then use them more than once. Don't spend NOT gates each time you need an inverted input.

I 'm not familiar with 40XX series. It's important knowledge, but I admit of not having acquired it yet. The 74XX series is more familiar to me and tested to be sturdy enough for educational purposes. They work ideally with 5V, but 3AA batteries will do most of the time. 2-input gates some in ICs of 4, 3-input gates come in ICs of 3 and inverters come 6 in each IC.

The switches used in the video are push-buttons, as you said. I would use double-pole double-throw switches, so I don't have to keep them pushed. Like these ones: http://img.diytrade.com/cdimg/860392/7969147/0/1301298514/No_lock_self-locking_switch.jpg
Another good thing about dual throw buttons is that they provide Ground as an input while OFF, not an open circuit, and IC inputs need to be tied to a voltage level at all times.

You can't use a numpad for your application, because you want to input binary, not decimal.

#### PG1995

Joined Apr 15, 2011
832
Thanks a lot.

I also want to use 74xx series. But which IC give 4 input OR gates. Please let me know. Thank you.

#### justtrying

Joined Mar 9, 2011
439
that was quite a question!

as far as I know there isn't a 4 input OR gate in 74xx, only 2 input.

#### PG1995

Joined Apr 15, 2011
832
Okay, then is this possible to make 4 input OR gate using 2 input OR gates? Please help me with it. Thanks.

#### Zazoo

Joined Jul 27, 2011
114
Okay, then is this possible to make 4 input OR gate using 2 input OR gates? Please help me with it. Thanks.
Yes. Three 2-input gates will work:

A+B+C+D = (A+B) + (C+D)

#### PG1995

Joined Apr 15, 2011
832
Thank you, GeoRacer, Justtrying, Zazoo.

The truth tables are all correct.

B function can be reduced to w+x'+y'z'+yz
C function can be reduced to w+x+y'+z
You forgot to group the minterm 5 for D
G function can be reduced to w+xy'+yz'+x'y

It takes some practice to notice the bigger groups.

You need only 4 inverters at max. You can create the inverted signals for the 4 inputs and then use them more than once. Don't spend NOT gates each time you need an inverted input.

I 'm not familiar with 40XX series. It's important knowledge, but I admit of not having acquired it yet. The 74XX series is more familiar to me and tested to be sturdy enough for educational purposes. They work ideally with 5V, but 3AA batteries will do most of the time. 2-input gates some in ICs of 4, 3-input gates come in ICs of 3 and inverters come 6 in each IC.

The switches used in the video are push-buttons, as you said. I would use double-pole double-throw switches, so I don't have to keep them pushed. Like these ones: http://img.diytrade.com/cdimg/860392/7969147/0/1301298514/No_lock_self-locking_switch.jpg
Another good thing about dual throw buttons is that they provide Ground as an input while OFF, not an open circuit, and IC inputs need to be tied to a voltage level at all times.

You can't use a numpad for your application, because you want to input binary, not decimal.
Special thanks to you for pointing out the mistakes in simplified expressions. I have corrected the mistakes in the new attachment. Please have a look to see if I'm still missing something. Sorry, I didn't highlight anything in the attachment this time.

I don't know why you say that I can't use numpad. Please have a look on this applet. If I want to display "9" then the input "a" and "f" should be HIGH. Okay. Suppose I have a numpad and take connections from the inputs "a" and "f" and connect them to the key 9 on the numpad so that when when key 9 is pressed on the numpad, the HIGH input goes to both "a" and "f" and we get "9" on the display. The numpad serves as the main interface and this way we can also get rid of those 'unwanted' displays which results from the pressing of invalid combinations of those four buttons. Do I make any sense?

I think I will use 7432 ICs to implement 4-input OR gates because 74xx series is easily available.

Which batteries should I use? 9V battery?

Thank you for all the help.

Best regards
PG

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#### Georacer

Joined Nov 25, 2009
5,182
I 'm not sure, but it's not so easy to interface with a real numpad. The last one I had worked with, was with an 8085 and had 7 pins, 3 for each column and 4 for each row. You had to scan row by row and see which column responded to find out which button was pressed.
If you find one that outputs 4-bit binary, go ahead.

As I said on my previous post, you can use 3xAA batteries to operate the 74XX.

Of course you should use two 2-input ORs to create the 4-input one.

I missed a simplification for F: you can group m:4,6,12,14
In function G, group w isn't necessary. Its 1s are covered by other groups.

I can't see anything else for now.

#### PG1995

Joined Apr 15, 2011
832
Thank you very much, GeoRacer.

I will use push-buttons; I was simply curious to know if it was possible to use a numpad.

For function G, you say that the group 'w' isn't necessary but, sorry, I don't see how. The two 1's in the last row aren't covered by any other group(s). So, what am I missing here? Please help me with it. Thanks.

Best regards
PG

#### Georacer

Joined Nov 25, 2009
5,182
Errata: I meant C. Minterms 8 and 9 are contained in both groups w and y'.

#### PG1995

Joined Apr 15, 2011
832
Thanks a lot.

I'm amazed how you were able to detect those errors in the K-maps! Once again, thanks.

Best wishes
PG

#### Georacer

Joined Nov 25, 2009
5,182
Practice, practice, practice.

Something I should do with my control systems problems too...