Simplifying Circuits I have a question regarding simplifying a circuit of a function below that has 5 logic gates in original.

f = (A + B) * (C + D) + (A + B) * (C + D)' + C

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

= (A + B) * 1 + C Complement

= (A + B) + C

Now, I have reduced to 2 logic gates from 5. But, here, am I allowed to change (A + B) + C to A + B + C, so that I can reduce number of gates (i.e., 1 logic gate) even more? If I am allowed, is there a name for this process (what kind of law is this)?

Thank you in advance.

• Previously asked at math.stackexchange.com/q/1126470/18398 – Joel Reyes Noche Jan 30 '15 at 13:04
• You should always link to multiple instances of the same question whenever you ask the same question on different StackExchange sites. – Joel Reyes Noche Jan 30 '15 at 13:04
• I assume that (A+B)*(C+D)' means ((A+B)*((C+D)'). Wouldn't your original need 6 logic gates? Did you count the NOT gate in (C+D)'? (Remember, you also have a (C+D) term.) – Joel Reyes Noche Jan 30 '15 at 13:08
• Also, what is the word "Complement" in the third line about? It seems like it shouldn't be there. – Joel Reyes Noche Jan 30 '15 at 13:10
• @JoelReyesNoche It's just a tag for complement law which states x+x'=1. – IANIK Jan 30 '15 at 13:21