I have to simplify the following boolean expression by proceeding only in POS form and not combining variables:
XYZD + X'P +Y'P + Z'P + D'P
Notation is
- . means AND
- + means OR
- ' means NOT
"." is omitted wherever unambiguous as AND has precedence over OR.
I am able to solve this by combining terms but it is not allowed :
= XYZD + P.(X'+Y'+Z'+D')
= XYZD + P.(XYZD)' (DEMORGAN LAW)
= (XYZD + P) . ( XYZD+ (XYZD)' ) (Distributive Law A+B.C = (A+B).(A+C) )
= (XYZD + P) . (1) *(Complementary Law)
= XYZD + P (IDENTITY)
Why do this :
- This is generally useful when someone has already simplified an expression to pos using boolean laws and we don't want to go backwards
- if we are given an intermediate form of a boolean expression to proceed with, combining variables is counter-intuitive and there should be an alternative way to solve considering single variables at a time.
For eg : I should not get stuck when i have done the following :
Minimize : x.y.z.d+(x.y.z.d)'.p
= x.y.z.d+((x.y.z)'+d').p DEMORGAN Law
= x.y.z.d+((x.y)'+z'+d').p DEMORGAN Law
= x.y.z.d+(x'+y'+z'+d').p DEMORGAN Law
= x.y.z.d+x'.p+y'.p+z'.p+d'.p DISTRIBUTIVE Law
= x.y.z.d+x'.p+y'.p+z'.p+d'.p
now how to proceed further ???