Question

Simplification of the Boolean expression AB + ABCD + ABCDE + ABCDEF yields which of the following results?

(a)  ABCDEF

(b)  AB

(c)  AB + CD + EF

(d)  A + B + C + D + E + F

(e)  A + B(C + D(E + F)) 

Answer 1

AB + ABC + ABCD + ABCDE + ABCDEF

=(AB +ABC) + (ABCD +ABCDE) + ABCDEF (Commutative Law Law)

=AB + ABCD +ABCDEF (Absorption Law)

=AB +( ABCD +ABCDEF) (Commutative Law Law)

=AB +ABCD (Absorption Law)

=AB

So, simplification of the Boolean expression AB + ABCD + ABCDE + ABCDEF yields AB