# 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?

Related Engineering and Comp Sci Homework Help News on Phys.org
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