I am designing a 4-bit comparator with a look ahead unit using a bit slice approach. I have to break the propagation of the Logical expressions for (A<B)i
and (A>B)i
. The main question is, could I use the following to simplify the boolean expressions.. The i is a subscript meaning the ith bit. The i-1 is a subscript meaning the bit before the ith bit.
(A<B)i = ~Ai*Bi + ~Ai*(A<B)i-1 + Bi*(A<B)i-1
Could I Take ~Ai
common from the first two expressions leaving me with
~Ai*(Bi + (A<B)i-1) + Bi(A<B)i-1
Let's call Bi + (A<B)i-1) = Q
And let's call ~Ai = P
I'm left with P*Q + Q
Using the boolean law that Q + Q*P = Q
Can I simplify the expression to just
(A<B)i = Bi + (A<B)i-1