Make Karnaugh maps for each of the seven expressions below, andfind a minimal Bo

Question

Make Karnaugh maps for each of the seven expressions below, andfind a minimal Booelean expression for each particular displacesegment.



A seven-segment display is used by simple calculators to display adigit 0-9 or the letters A-F. Using 4 inputs w, x, y, z ,to represent the numbers 0-15 in binary (so e.g. y = 1 and w = x =z = 0 represents 2), make a table with 16 rows and 4+7 columns.Write w, x, y, z, a, b, c, d, e, f, g as the heading ofthe 11 columns. Fill in the first 4 columns with the binary numbersof 0-15, expressions for each of the seven segments a, b, c, d,e, f, g (the segments are labeled starting from the topsegment clockwise and the segment in the middle is g)

A seven-segmentdisplay : Truth Table : Decimal
Number Inputs Outputs              w x y z a b c d e f   0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 0
0
0
0
0
0
0
0
1
1
1 1 1 1 1 1 0
0
0
0
1
1
1
1
0
0
0 0 1 1 1 1 0
0
1
1
0
0
1
1
0
0
1 1 0 0 1 1 0
1
0
1
0
1
0
1
0
1
0 1 0 1 0 1 1
0
1
1
0
1
1
1
1
1
1 0 1 1 1 1 1
1
1
1
1
0
0
1
1
1
1 0 0 1 0 0 1
1
0
1
1
1
1
1
1
1
1 1 0 1 0 0 1
0
1
1
0
1
1
0
1
1
0 1 1 1 1 0 1
0
1
0
0
0
1
0
1
0
1 1 1 1 1 1 1
0
0
0
1
1
1
0
1
1
1 1 1 1 1 1 0
0
1
1
1
1
1
0
1
1
1 1 1 0 1 1 A seven-segmentdisplay : Truth Table : 5
6
7
8
9
10 11 12 13 14 15 0
0
0
0
0
0
0
0
1
1
1 1 1 1 1 1 0
0
0
0
1
1
1
1
0
0
0 0 1 1 1 1 0
0
1
1
0
0
1
1
0
0
1 1 0 0 1 1 0
1
0
1
0
1
0
1
0
1
0 1 0 1 0 1 1
0
1
1
0
1
1
1
1
1
1 0 1 1 1 1 1
1
1
1
1
0
0
1
1
1
1 0 0 1 0 0 1
1
0
1
1
1
1
1
1
1
1 1 0 1 0 0 1
0
1
1
0
1
1
0
1
1
0 1 1 1 1 0 1
0
1
0
0
0
1
0
1
0
1 1 1 1 1 1 1
0
0
0
1
1
1
0
1
1
1 1 1 1 1 1 0
0
1
1
1
1
1
0
1
1
1 1 1 0 1 1 Decimal
Number Inputs Outputs              w x y z a b c d e f   0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 0
0
0
0
0
0
0
0
1
1
1 1 1 1 1 1 0
0
0
0
1
1
1
1
0
0
0 0 1 1 1 1 0
0
1
1
0
0
1
1
0
0
1 1 0 0 1 1 0
1
0
1
0
1
0
1
0
1
0 1 0 1 0 1 1
0
1
1
0
1
1
1
1
1
1 0 1 1 1 1 1
1
1
1
1
0
0
1
1
1
1 0 0 1 0 0 1
1
0
1
1
1
1
1
1
1
1 1 0 1 0 0 1
0
1
1
0
1
1
0
1
1
0 1 1 1 1 0 1
0
1
0
0
0
1
0
1
0
1 1 1 1 1 1 1
0
0
0
1
1
1
0
1
1
1 1 1 1 1 1 0
0
1
1
1
1
1
0
1
1
1 1 1 0 1 1

Explanation / Answer

Dear, Sum of products functions : Simplifythe output varibles by using K-map method then we get followingequations.          
          a =w'x'z'+w'y+xz+wx+wy'z+yz'           b= x'+w'y'z'+w'yz+wy'z
          c= w'y'+w'x+w'yz+wy'z+wx'           d= w'x'z'+xy'z+wy'+wx'z+xyz'           e= yz'+wy+wz'+w'x'z'           f =w+y'z'+xyz'           g= wx'+yz'+wz'+xy'z'+w'x'y
I hope this is helpful foryou.................

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