# Simple boolean simplification - can i simplify it further?

## Homework Statement

F(A,B,C,D) = (sum of) m (2,3,5,7,11,13)
Design a two level network to implement the above sum of products:

## Homework Equations

F(A,B,C,D) = (sum of) m (2,3,5,7,11,13)

## The Attempt at a Solution

Code:
K-map
___Ab
CD|00..01..11..10
00|
01|1...1....1
11|1...1.........1
10|

My attempted solution:
F = CA' + CDB + CD'B'
F = CA' + C (DB + D'B')
F = CA' + C(D xor B)'
F = CA' + CD xor CB'

now can i factor out the C? This has to be two level so I'm thinking it'd take up two different blocks of logic gates.

Any help?

What is a two level network may I ask?

the last line of it should be: F = C (A' + D xor B')

Since all have C in common. I'm probably wrong though.

OK. I found what the definition of a two-level circuit is: the implementation of a Boolean function with NAND gates is simplest if the function is in sum-of-products form. This form corresponds to a two-level circuit.

So, as a sum of products, I get that F = BC'D + A'BD + B'CD + A'B'C. You should be able to quickly draw the two-level circuit from it using NAND gates without any problems.

thanks a tonne i managed to figure it out a while back.
thanks