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I have a subject called computer architecture in university but I don't get a clue of it. We get assignments like: make a 2-bit two’s complement carry lookahead adder using 3 4-bit adder.

This is a circuit I have to make in Logisim, however, it's like you need an already deep insight in the subject to be able to make this; insights I don't have (because it's totally new for me).

Is there a kind of method to solve and make these circuits? Using truth tables or anything?

Note: I'm not asking for the solution for this specific problem, only for a method or steps-to-take in general, to be able to make any (basic) circuit.

This is the full exercise: http://msdl.cs.mcgill.ca/people/hv/teaching/ComputerSystemsArchitecture/materials/CA2/CA_Project_2.pdf (Ex5 if you want more explanation of the problem).

I was able to solve the other 4 by trying very hard and using Google but without actually knowing what I was doing.

So again, I'm not asking for this specific solution, only if there is a general way to solve these kind of assignments using a specific method or steps, eventually explained by using this one example-exercise.

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    $\begingroup$ There is en.wikipedia.org/wiki/Logic_synthesis but the general way of solving exercises in university is by understanding the material or asking your TAs if you have problems. $\endgroup$ – adrianN Oct 27 '17 at 8:25
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    $\begingroup$ Work with your peers. Students manage to pass the class somehow, so there must be a principled way. The course is designed to impart the mode of thinking which enables you to solve such exercises, but unfortunately the only way to accomplish this is by actually solving the exercises, on your own or together with friends. $\endgroup$ – Yuval Filmus Oct 27 '17 at 9:22
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Both suggestions in the comments in the OP were excellent and I agree with the users who provided them. I have included these comments below for continuity:

There is en.wikipedia.org/wiki/Logic_synthesis but the general way of solving exercises in university is by understanding the material or asking your TAs if you have problems. – adrianN

Work with your peers. Students manage to pass the class somehow, so there must be a principled way. The course is designed to impart the mode of thinking which enables you to solve such exercises, but unfortunately the only way to accomplish this is by actually solving the exercises, on your own or together with friends. – Yuval Filmus

To assist you, look at the Wikipedia pages here and here on digital circuits/adders.

Also, ask your instructor and/or TA for suggestions on a good computer architecture and design book.

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