Truth Tables Help

My earlier post should read: I have a four part question in a tutorial, parts 1 & 2 I don't have any problem with. Parts 3 & 4 I have no idea what they mean. Can someone explain to me what parts 3 & 4 mean and how can I answer the questions. Alternatively if you can point me to a website that might be of some help. The question: Draw the truth tables for each of the following expressions:

1. AB'CD' + ABC'D' + A'BC'D + A'B'CD
2. (A + B' + C' + D)(A' + B + C + D')
3. Sigma m(2.5.6.9)
4. Pi M(0,7,10,11)

3 & 4 should read: _ \ /_ m (2.5.6.9)

__ I I M (0,7,10,11) Appreciate any help. TIA

What do your texts or lecture notes say these notations mean? Guess: Sigma indicates + over some set, and Pi indicates . over some set--but what sets?

If I recall correctly Sigma is usually successive addition and the big PI is usually a successive multiplication.

in article 416ec436$0$59435$ snipped-for-privacy@ptn-nntp-reader03.plus.net, BIGEYE at snipped-for-privacy@ddres.is.invalid wrote on 10/14/04 11:23 AM:

Whenever I note that the use of language skill in engineering is a valuable asset, I get put down. Here is an example of a problem that is poorly posed and communicated. I have no idea what anything after the colon signifies.

I can only guess that earlier in the tutorial there was a discussion of symbology to be used in the remainder of the tutorial. Without knowing what that is, I have no idea on how to help.

Bill

Hello,

Most likely, the sigma notation is a compact form of writing a Boolean equation in the form of question one. Looking at question one, every place the equation evaluates to one/true (1010, 1100, 0101, 0011) the input value is placed in the sigma. In Boolean algebra/digital design, OR essentially (for one bit) acts as addition (AND as multiplication), hence the sigma (summation over a period)/pi (product over a period) notation. So problem one could be written as Sigma m(3, 5, 10, 12).

Most likely, the big pi notation corresponds to a Boolean equation in the form of question two and is similar to the sigma notation except the pi notation uses AND (one bit multiplication) rather than OR (one bit addition).

As I have seen it in digital design courses I have taken, the sigma/pi notation is commonly used when working with karnaugh maps, or k-maps for short. A k-map is a method for simplifying a Boolean equation.

I don't know of a good website, but any undergraduate digital design textbook should provide an in-depth discussion of the subjects you are looking to learn about. If your really looking for a website, you could try searching for 'digital design', 'Boolean algrbra', karnaugh maps', etc if you already haven't.

Note two things: addition and multiplication of binary values does not simply correspond to AND and OR. Also, this is the way I have commonly used, and seen used, the sigma/pi notation. There could be other interpretations.

Hope this helps.

Scott

Problem with is parts 3 & 3. Parts 1 & 2 read

1. (A and not B and C and not D) or (A and B and not C and not D) or ( not A and B and not C and D) or (not A and not B and C and D)
2. (A or not B or not C or D)(not A or B or C or not D)

First line should have read 3& 4

at

Yes, but addition of what in this case, and multiplication of what in this case?

Exactly, so what, according to your text or notes, do Sigma(2.5.6.9) and Pi(0,7,10,11) mean?

I believe I remember the terminology sum of maxterms and product of minterms from a digital design class several years ago. I don't remember exactly what they mean.