DOB seven segment display

Thread Starter

axel1111

Joined Apr 20, 2011
2
iam getting confused on this problem in my homework in which all you have to do is display your DOB on 1 seven segment display by cycleing through them with three switches in binary. I am getting stuck at where it says "write the simplified Sum-Of-Products Boolean equations forthe seven outputs a, b, c, d, e, f, & g."

My truth table is here:http://pastebin.com/UuKatSvZ

(using pastebin so everything is still inline)

so my question is how would i write out the SOP equation for a,b,c,d,e,f & g?
 

Georacer

Joined Nov 25, 2009
5,182
Ok, let's describe it in a different way:

We know that the 7-seg display must show a predefined symbol for each different combination of its 3-bit input.
We 'll take it a bit further and say that each separate segment must be either ON or OFF for each of the 8 different inputs. Isn't that a standart boolean function that takes the value 0 or 1 depending on 3 input variables X, Y and Z?
And since we have 7 segment, we have 7 boolean functions in our hands.
For each function, a digital circuit must be built in order to drive the respective segment.

I 'll give you the example of the "a" segment, based on your image attachment:
Let the function A represent the boolean function that will describe the operation of the "a" segment.
A(X,Y,Z)=Σ(2,5).
After the simplification (which in this case is non-existent), that becomes:
A=X'YZ'+XY'Z.
That is the function which after being implemented into a circuit, will drive the "a" segment.

Is that clear?
 
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