Simplify Boolean Algebra Expression

WBahn

Joined Mar 31, 2012
29,522
¬A.¬B.¬C + A.B.¬C + A.¬B.C + A.B.C what is this in its simplest form
First, this is a homework problem and so answers aren't supposed to be just given out.

Second, as pointed out earlier, it depends on what the metrics are for "simple".

For instance, which is "simpler", (A(BC)')' or A' + BC ?

What are your metrics?
 

WBahn

Joined Mar 31, 2012
29,522
It's A' + BC, just to keep us on the same page.

Why do you say that this is "simpler"? Again, what metric are you using to decide when one expression is "simpler" than another.

Using basic CMOS logic gates, the expression (A(BC)')' requires a 2-input NAND gate and a 2-input NOR gate which requires eight transistors and incurs two gate delays from input to output. The expression (A'+BC) requires an inverter, an AND gate, and an OR gate which total to fourteen transistors and four gate delays. So it is nearly twice as large and only half as fast. Is it still "simpler"? Depends on what your metrics are.
 

WBahn

Joined Mar 31, 2012
29,522
i need whatever has the least amount of gates
What gates are you limited to? To match Boolean algebra, that would be NOT, AND, and OR in any width (so a 12 input AND gate would be legal). Or are you limited to 2-input gates? Are you limited to NOT, NAND, and NOR? This is a common limitation in the real world along with a maximum on the number of inputs to any one gate, often in the four range. Can you use XOR?

In engineering, the answer is usually, "It depends," until all of the constraints are adequately established.
 

WBahn

Joined Mar 31, 2012
29,522
yes xor can be used and were not limited to any gates
Okay, so then you need to show YOUR work on YOUR homework problem. And, actually, you need to keep in mind that this is the OP's thread and that you are technically hijacking it, but at least you are talking about the OP's original problem. So show your work and you and the OP can collaborate and we can provide hints and suggestions. We will not just give out answers.

The main hint that you need to incorporate an XOR gate is contained in Post #9.
 

djsfantasi

Joined Apr 11, 2010
9,131
Listen, he is not the one being rude. He is following the rules of this section, which you have read presumably.

In order to receive help here, you are required to show your work. That is so we can understand your question better, can see where you are getting stuck and answer appropriately.
 
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