# Standard Product of Sums Question

Discussion in 'Math' started by paper.airplane, Nov 30, 2010.

1. ### paper.airplane Thread Starter New Member

Nov 30, 2010
2
0
Hi everyone,

(It starts at around this part
I understand how to calculate the SPOS, but I don't understand the logic behind the example they give.

The answer is (A + B + C) (A' + B' + C') and I know we want the sensors to detect the flame equally. So why is it that A OR B OR C logic works? Shouldn't it be A AND B AND C? Because then A and B and C would have to be equal for the output to be 0, which is what we want right?

I'm sorry if I don't make sense, English isn't my first language, so if you have any questions, please ask. Thanks in advance!

2. ### StayatHomeElectronics Well-Known Member

Sep 25, 2008
864
40
That portion of the example is for "sensor agreement" not for the "flame detection." What they are showing in the truth table is that when all three sensors are '0' or all three are '1' that the sensors are in agreement and that the sensors all appear to be working. The output of '0' when the sensors are in agreement shows that no alarm is activated.

3. ### paper.airplane Thread Starter New Member

Nov 30, 2010
2
0
I understand now, I just re-read the section and it's all clear now. thanks!