hej
I am having trouubles with understanding from where the Boolean equations come from.

Link: http://www.allaboutcircuits.com/vol_4/chpt_9/5.html

to

What is the method of interpreting the matrix and converting it to boolean expression for each segment.

Thanks for your time

 

Take note of the segment notation in the display article - http://en.wikipedia.org/wiki/Seven-segment_display

Relate the lit segments to the number being displayed.

 

I get this... I have made 7-segment display in 2 different ways...
1st was that I took each segment as a boolean function and than I made minimal normal form for each segment. The "screen" showed the indexes of entering minterm vector; the values form 10-15 were reserved for letter E.

It worked but it took me 65 NOT, AND and OR gates + It wasnt very efficient

2nd way was that I first made 4/11 decoder wich decoded input vector to 11 different exits. Each exiting vector had a minterm property (one of the exitst is always 1 and the others are 0)

Than I made a encoder wich encoded 11 values to 7 values...
1st I did it with a use of standard values of encoder's input vector. I combined them with OR gates.
2nd I did it with the negated input vector and with AND gates...
I found out that 2nd method is in this case better.

I am having troubles because at the lecture from Basics of digital circuits the professor said that the input of the encoder must be a vector with minterm properties, meaning only I input can be 1 and the others must be 0.

If we have this the boolean equation is in form y=m v& C
where
y is output vector
m in entering minterm vector
C coding matrix

So from where do I get an equation for first segment (D_0) . What do I have to look for? Do I have to look where the value in coding matrix is 1?
Can somebody explain me how did we get the equation for the first one and I will try to extract the method from it.

Thanks for your time

 

I got it...
For segment 1(D_0) the value is 0 in case if the value of input vector is 0 0 0 1 or 0 1 0 0 . From here I see that the value is of first and third digit are always 0.
But here is a problem..if I would only take this the values would also be 0 when input vector would be 0 0 0 0 and 0 1 0 1 so I must exclude them. I do this with the second half of the boolean equation.

now i got it

 

Take a look at the data sheet for a 7 segment decoder IC like a 74LS47.