A
Logic Problem
A common way to display a result of a digital calculation is with a seven
segment display. The way the seven segment display is used is shown
below.
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A four bit input signal
forms the input to the seven segment decoder.
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The output of the decoder
is seven signals to drive the seven segments of the display.
The problem here is to design the logic circuit for the seven segment decoder.
To get you started we will give you the truth table for one segment, the
top segment. (Call that segment A with a corresponding Boolean variable,
A.) Check the truth table to be sure that it is correct.
Take note of the Don't Cares in the truth table!
|
I8
|
I4
|
I2
|
I1
|
A
|
|
0
|
0
|
0
|
0
|
1
|
|
0
|
0
|
0
|
1
|
0
|
|
0
|
0
|
1
|
0
|
1
|
|
0
|
0
|
1
|
1
|
1
|
|
0
|
1
|
0
|
0
|
0
|
|
0
|
1
|
0
|
1
|
1
|
|
0
|
1
|
1
|
0
|
1
|
|
0
|
1
|
1
|
1
|
1
|
|
1
|
0
|
0
|
0
|
1
|
|
1
|
0
|
0
|
1
|
1
|
|
1
|
0
|
1
|
0
|
X
|
|
1
|
0
|
1
|
1
|
X
|
|
1
|
1
|
0
|
0
|
X
|
|
1
|
1
|
0
|
1
|
X
|
|
1
|
1
|
1
|
0
|
X
|
|
1
|
1
|
1
|
1
|
X
|
-
For this truth table,
find the function when all of the Don't Cares
(marked with X's) are counted as ones.
-
For this truth table,
find the function when all of the Don't Cares are counted as zeroes.
Compare the complexity of this function with the function found when the
Don't Cares are counted as ones.