A(X,Y,Z) = Σm(0,1,7)
Truth table:
X Y Z
|
0
|
0
|
0
|
|
0
|
0
|
1
|
|
0
|
1
|
0
|
|
0
|
1
|
1
|
|
1
|
0
|
0
|
|
1
|
0
|
1
|
|
1
|
1
|
0
|
|
1
|
1
|
1
|
Sum of products Expression :
X’Y’Z’+X’Y’Z+XYZ
K-Map :
Simplified karnaugh Map equation :
X’Y’+XYZ
=X’Y’(Z+Z’) + XYZ
= X’Y’Z+X’Y’Z’+XYZ
2.A(X,Y,Z) = Σm(2,3,4,5,6)
|
X
|
Y
|
Z
|
A
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
1
|
|
0
|
1
|
1
|
1
|
|
1
|
0
|
0
|
1
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
0
|
Sum of products Expression :
X’YZ’+X’YZ+XY’Z’+XY’Z+XYZ’
K-Map :
Simplified karnaugh Map equation :
XY’+X’Y+YZ’
=XY’(Z+Z’) + X’Y(Z+Z’) + YZ’(X+X’)
=XY’Z+XY’Z’+X’YZ+X’YZ’+XYZ’+X’YZ’
=XY’Z+XY’Z’+X’YZ+X’YZ’+XYZ’
X’YZ’+XYZ’
3.A(X,Y,Z) = Σm(2,6)
|
X
|
Y
|
Z
|
A
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
0
|
1
|
|
0
|
1
|
1
|
0
|
|
1
|
0
|
0
|
0
|
|
1
|
0
|
1
|
0
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
0
|
Sum of products Expression :
X’YZ’+XYZ’
K-Map :
Simplified karnaugh Map equation :
YZ’
=YZ’(X+X’)
=XYZ’+X’YZ’
4.A(X,Y,Z) = Σm(1,2,3,5,6,7)
|
X
|
Y
|
Z
|
A
|
|
0
|
0
|
0
|
0
|
|
0
|
0
|
1
|
1
|
|
0
|
1
|
0
|
1
|
|
0
|
1
|
1
|
1
|
|
1
|
0
|
0
|
0
|
|
1
|
0
|
1
|
1
|
|
1
|
1
|
0
|
1
|
|
1
|
1
|
1
|
1
|
Sum of products Expression :
X’Y’Z+X’YZ’+X’YZ+XY’Z+XYZ’+XYZ
K-Map :
Simplified karnaugh Map equation :
Y+Z
=Y+Z(X+X’)
=YX+YX’+ZX+ZX’
=(YX+YX’)(Z+Z’) + (ZX+ZX’)(Y+Y’)
= XYZ+X’YZ+XYZ’+X’YZ’+XYZ+XY’Z+X’YZ+X’Y’Z
= XYZ+X’YZ+XYZ’+X’YZ’+XY’Z+X’Y’Z