• Support PF! Buy your school textbooks, materials and every day products Here!

Simple boolean simplification - can i simplify it further?

  • Thread starter trickae
  • Start date
  • #1
83
0

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?
 

Answers and Replies

  • #2
1,357
0
What is a two level network may I ask?
 
  • #3
3
0
the last line of it should be: F = C (A' + D xor B')

Since all have C in common. I'm probably wrong though.
 
  • #4
1,357
0
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.
 
  • #5
83
0
thanks a tonne i managed to figure it out a while back.
thanks
 

Related Threads on Simple boolean simplification - can i simplify it further?

  • Last Post
Replies
5
Views
1K
Replies
2
Views
466
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
10
Views
574
  • Last Post
Replies
5
Views
8K
  • Last Post
Replies
10
Views
5K
  • Last Post
Replies
1
Views
299
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
1
Views
2K
Top