Karnaugh map help

jclfc

Hi,

I have a question here that says: Show how the following expression was obtained from a K-Map:

BD + /B/D

Am I right in thinking that the answer to that question would be to make a K-Map w so that the answer is the above? Would I need to add anything else?

Also, how on Earth do I go about simplifying the following using a K-Map?

ABCD X
0000 1 1000 1
0001 1 1001 1
0010 X 1010 0
0011 0 1011 0
0100 1 1100 1
0101 1 1101 1
0110 X 1110 0
0111 1 1111 0


I would be grateful for any help!

pauln

I'll take a stab at the second one:

Your Karnaugh map for that table of values would look like,

ab\cd 00 01 11 00
00

---

1--1--0--*
01

---

1--1--1--*
11

---

1--1--0--0
00

---

1--1--0--0

That gives two over-lapping groups, one group of eight being columns 1&2 and one group of four being row 2.
The group of eight works out as |C and the group of four comes to |A*B

Giving your espression as X= |C + |A*B (|=NOT)

I've no real idea about the first one, maybe one of the others will know better, my experience of these has been pretty limited to date.

jclfc

Cheers for that mate.

How about this -

Simplfy the following expression with K-Map -

1. A/BC + ABC + /ABC + /AB/C

pauln

1. A/BC + ABC + /ABC + /AB/C
Three variables, ABC
The truth table would be:

A B C--X
0 0 0--0
0 0 1--0
0 1 0--1
0 1 1--1
1 0 0--0
1 0 1--1
1 1 0--0
1 1 1--1

From this the karnaugh map is:

A\BC 00 01 11 10
0

---

0--0--1--1
1

---

0--1--1--0

Edit: (Removed one solution because it used more groups then necessary)

From this you can create two groups of two 1's. One in row 1. one in row 2.

The first group solves as, |A*B
The second as, A*C

Giving simplified expression as X=|A*B + A*C

jclfc

Cheers again mate. Your edit was the answer I come up with so I'll stick with that.

Only one I got left now is to show how X = BD + /B/D was obtained from a KMap.

Any idea whatsoever?

pauln

After having a look around I came up with something that says to reverse the simplification by applying the Distributive law in reverse to expand the function and replace missing mid-terms, or something along those lines?
All gibberish to me I'm afraid.

Michael Collins

I think what that first question is getting at is to see if you understand Karnaugh maps. It's all very well being able to solve these mysterious blocks of 1s and 0s but you should understand how it works. Why? 1) To show intelligence, 2) what happens when you have more that 4 variables? 3D Karnaugh maps! And more still?

Bascially what these maps do is simplfy the implementation of the following Boolean identities:

A+|A=1
A+A=A