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Logic circuit, logic function, minimized function, minimized circuit

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Phuckie

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Hello, guys! I have a homework in Digital Desing (logic circuits, logic functions, minimized functions, minimized circuits etc.) and I want your help.

For the following circuit:
1) Compute: a) The Truth Table, b) The logic function.
2) The minimized function in sum of products form.
3) Design the minimized circuit corresponding to the logic function of 2) by
using only: a) NOR gates, b) XOR gates.
**broken link removed**

Solution:
1) a)
**broken link removed**

b) Logic Function: F = 1

2) Minimized function in SOP form: F = 1

Could you please check my solution till then? Is my solution ok? What about the 3rd question? How can I design the minimized circuit corresponding to the logic function of 2) by using only: a) NOR gates, b) XOR gates.
 
do steps

Hi. You solve this by adding several coloumns and having more than just one function.
 

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Grossel, I didn't understand. I solved the 1st question (a. truth table and b. logic function) and I uploaded the truth table, as you can see. I want help in the 3rd question.
 
Ok. If you're sure solution is correct, you only need one nand gate and one xor gate because any inputs won't have no effect.
 
"How can I design the minimized circuit corresponding to the logic function (F=1) of question 2) by using only: a) NOR gates, b) XOR gates."

Why do I need a NAND gate and a XOR gate? Could you please draw the circuits of a) and b)? I don't understand you, sorry.
 
Last edited:
"How can I design the minimized circuit corresponding to the logic function (F=1) of question 2) by using only: a) NOR gates, b) XOR gates."

Why do I need a NAND gate and a XOR gate? Could you please draw the circuits of a) and b)? I don't understand you, sorry.
Na. Frankly you doesn't need a gate. A wire would work properly to this do the function. Spending a physical gate on that is just a big waste.

If you don't understand, I show:
 

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Phukie,

Your derivation of the logic function is flawed. The correct equation is shown below. Once you figure out the correct logic equation, you can use the program I wrote in the attachment below to get the minterms. Make sure you read the program instructions carefully. Then use a Karnaugh map (K-map) and plug in the minterms to get the best reduction. Afterwards, by the method shown in any logic book, you can also change the logic gate functions to see what gives you the least parts count, least cost, simplest circuit, etc. According to the K-map, the logic function reduces to C+D' .

This is the logic function of your problem (AB')'(B'C)(C+D)+C(C+D+D)+D' where ' means "not". You should confirm its correctness and learn how to do it yourself.

Ratch
 

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Thanks for the answers guys. Ratchit, are you sure that the logic function is: (AB')'(B'C)(C+D)+C(C+D+D)+D' ? I found (AB')'(B'C)(C+D)+C(C+D+D)+C'.
 
Phukie,

Ratchit, are you sure that the logic function is: (AB')'(B'C)(C+D)+C(C+D+D)+D' ? I found (AB')'(B'C)(C+D)+C(C+D+D)+C'.

Yes, you are correct. I crossed over the C and D line. That makes the function equal to 1. Good, you do know how to evaluate the logic function.

Ratch
 
Ratchit, I had written this logical expression in the truth table (first post). Ok! Now how can I design the minimized circuit corresponding to the logic function (F=1) of question 2) by using only: a) NOR gates, b) XOR gates ? Do you have any ideas?
 
Phuckie,

Ratchit, I had written this logical expression in the truth table (first post). Ok! Now how can I design the minimized circuit corresponding to the logic function (F=1) of question 2) by using only: a) NOR gates, b) XOR gates ? Do you have any ideas?

As Grossel showed you, a wire is all you need, and that is just about as minimal as you can get.

Ratch
 
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