Answer to Question #234643 in Discrete Mathematics for ndcjbcfv

Question

Boolean expressions to minimal number of literals:

1. x'y' + xy + x'y

2. (x + y) (x + y')

3. x'y + xy' + xy + x'y'

4. x' + xy +xz' + xy'z'

5. A'C' + ABC + AC'

6. (x'y' + z)' + z + xy + wz

7. A'B (D' + C'D) + B (A + A'CD)

Answer 1

1) x'y'+xy+x'y=x'(y'+y)+xy=x'+xy

2) (x+y)(x+y')= xx+xy'+xy+yy'=x+xy'+xy+yy'=x(1+y')+xy=x+xy=x(1+y)=x

3) x'y+xy'+xy+x'y'=x'(y+y')+x(y+y')=x'+x=1

4) x'+xy+xz'+xy'z'= x'+xy+xz'(1+y')=x'+xy+xz'

5) A'C'+ABC+AC'=C'(A'+A)+ABC=C'+ABC=(C'+C)(C'+AB)=C'+AB

6) (x'y'+z)'+z+xy+wz=(x'y')'.z'+z+xy+wz={(x+y).z'+z}+xy+wz=(x+y+z)(z+z')+xy+wz=x+y+z+xy+wz=x+xy+y+z+wz=x(1+y)+y+z(1+w)=x+y+z

7) A'B(D'+C'D)+B(A+A'CD)=B{A'(D'+C'D)+(A+A'CD)}=B{A'D'+A'C'D+A+A'CD}=B{A'D'+A+A'D'(C'+C)}=B(A'D'+A+A'D')=B{A'(D'+D)+A}=B(A'+A)=B