Changing 3 input or gates into 2 input xnor gates

  • Thread starter lalosfire
  • Start date
  • #1
lalosfire
1
0
Realize (a'b'c'+a'bc+ab'c+abc') using only 2-input x-nor gates.

I've taken a shot at this, however I'm only able to but it into more or gates.
a'(b'c'+bc)+a(b'c+bc')
a'[(b'+c)(b+c')]+a[(b'+c')(b+c)]
a'(b'c+bc')+a(b'c'+bc)
That's where I got, however it's really no simpler and I doubt is even close to being on the right track.
 

Answers and Replies

  • #2
CWatters
Science Advisor
Homework Helper
Gold Member
10,545
2,317
It's not far off.

Your first equation is...

a'(b'c'+bc)+a(b'c+bc') ......(1)

Then you seem to have missed that the first part on the left is in the right form for an XNOR.

An XNOR performs the function (x'y'+xy) so perhaps leave the bit a'(b'c'+bc) alone. That would make your second equation...

a'(b'c'+bc) + a[(b'+c')(b+c)] ......(2)

Now over to you to have another go. Leave the left hand side alone.
 
  • #3
CWatters
Science Advisor
Homework Helper
Gold Member
10,545
2,317
Aside:

I've found it helpful to remember DeMorgans rule as "split/join the bar and change the sign" also remembering that adding two inverters in series has no effect.

For example to manipulate x.y you can do the following steps..

x.y

Invert twice..

= (x.y)''

then split the lower bar and change the . to +

= (x'+y')'
 

Suggested for: Changing 3 input or gates into 2 input xnor gates

Replies
12
Views
270
  • Last Post
Replies
4
Views
518
  • Last Post
Replies
23
Views
1K
  • Last Post
Replies
12
Views
883
  • Last Post
Replies
1
Views
743
Replies
5
Views
61
  • Last Post
Replies
9
Views
699
Replies
32
Views
1K
  • Last Post
Replies
2
Views
191
  • Last Post
Replies
3
Views
679
Top