Simplying the circuit into Boolean expressions [2 Questions]

• Engineering
• lunapt
In summary, the conversation is about two questions involving simplifying logic expressions. The first question involves the expression (AB.CD) + [(CD)' . (AB)'] and the user is unsure how to simplify it further. The second question is about the expression A' + (D'+C') + A + (A' + C'+ D') + B' .D ' + (D+B)' = F and the user is not sure if it is correct and asks for help. The responder suggests using a truth table to check the working and advises to present one question at a time for better help.
lunapt
Question 1: http://imgur.com/Px0n152
Question 2: http://imgur.com/tZ0beF6

For Question 1, I got:

(AB.CD) + [(CD)' . (AB)'] with a "." = multiplication and ' = complement.
into (AB.CD) + [(CD+AB)']

I"m not sure how to simplify this further.

Question 2 is really long and I would appreciate help. I got:
A' + (D'+C') + A + (A' + C'+ D') + B' .D ' + (D+B)' = F

I'm not even sure if this is correct, and these two questions are due as homework tonight.

Any help would be much appreciated, thank you.

Hi lunapt. At any line in your working you yourself can check that you are proceeding correctly by drawing up a truth table for that line. Compare it with the truth table for the original logic, and they must agree at all times, right up to including your answer.

By not providing your earlier working, you don't allow us to identify whether the line you show has been arrived at correctly or not, or even whether it is your own effort. So can you show how you obtained that line?

Good luck! The simplified expression could not be much simpler.

BTW, it is best to present only one question, as it is likely that the help you receive with it will enable you to go on and solve other similar ones.

What is the purpose of simplifying a circuit into Boolean expressions?

The purpose of simplifying a circuit into Boolean expressions is to reduce the complexity of the circuit and make it easier to analyze and understand. This can also help in reducing the number of components needed and improve the efficiency and speed of the circuit.

What are some common methods used to simplify a circuit into Boolean expressions?

Some common methods used to simplify a circuit into Boolean expressions include Boolean algebra, Karnaugh maps, and Quine-McCluskey method. These methods involve manipulating Boolean expressions using logical operations such as AND, OR, and NOT to reduce them to their simplest form.

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