(a) (A + C)(C + D)
= (A + BB’ + C + DD’)(AA’ + BB’ + C + D)
= (A + B + C + D)(A + B’ + C + D’)(A + B + C + D)(A’ + B’ + C + D)
By removing duplicate terms we get canonical Product-of-Sum form:
(A + B + C + D)(A + B’ + C + D’)(A’ + B’ + C + D)
F = π(0, 5 , 12)
F = M0 + M5 + M12
(b) (X + Y)(Y + Z)(X + Z)
= (X + Y + ZZ’)(XX’ + Y + Z)(X + YY’ + Z)
= (X + Y + Z)(X + Y + Z’)(X + Y + Z)(X’ + Y + Z)(X + Y + Z)(X + Y’ + Z)
By removing duplicate terms we get canonical Product-of-Sum form:
(X + Y + Z)(X + Y + Z’)( X’ + Y + Z)( X + Y’ + Z)
F = π(0, 1 , 2, 4)
F = M0 + M1 + M2 + M4