Disjunctive Normal Form

Question

The boolean expression:

y= (a'+b) * (b(c'+d')) = (a'+b) * (bc' + bd')

is given.

Find out the disjunctive normal form to this boolean expression.

My suggestion:

y= a'bc'd' + a'bc'd + a'bcd' + abc'd' + abc'd+abcd'

only when these terms are true the function is 1 and otherwise not. (=0)

Is the DNF right?

Thanks for the help.

Edit: Here ist the truth table for the boolean expression:

Answer 1

That looks good your original equation reduces to (bc' + bd') which is what you have put in your truth table and then extracted in DNF.

Edit to clarify reduction of original equation.

(a'+b) * (bc' + bd')= a'(bc' + bd')+b(bc' + bd')

              = a'(bc' + bd')+(bc' + bd')

              = (bc' + bd')