logiccomputer-sciencecpu-architecturecircuitdigital-logic
How to simplify circuits
The answer to the question is A in case someone thinks Im cheating for a test or something. I really wan't to understand how to solve such questions. I am guessing there is some way to bring these brackets together and to get a simplified circuit but I don't understand it fully. Maybe something regarding truth tables?
Solution
abc' + a'bc' + a'b'c' + ab'c' initial expression
= (a + a')bc' + a'b'c' + ab'c' distributive law
= (T)bc' + a'b'c' + ab'c' additive inverse
= bc' + a'b'c' + ab'c' multiplicative identity
= bc' + (a' + a)b'c' distributive law
= bc' + (T)b'c' additive inverse
= bc' + b'c' multiplicative identity
= (b + b')c' distributive law
= (T)c' additive inverse
= c' multiplicative identity
The expression is equivalent to the inverse of c and so one logic gate is enough.
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