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:
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:
3 & 4 should read: _ \ /_ m (2.5.6.9)
__ I I M (0,7,10,11) Appreciate any help. TIA
I worked out 1 and 2 and found a shortcut I should have used once I was halfway done. Oh well.
Capital Sigma means sum. Example: [Cap. Sigma x] means, in Stats, the sum of all x values. [Cap. Sigma x^2] is the sum of the squares of all x values. You knew that, I imagine.
Outside of Stats, Cap. Sigma is an iterated sum. Example: Draw a Capital Simga on the chalkboard. Below it, write "n = 1". Above the Sigma, write 12. To the right of the Sigma, write "(2n-1)". The resulting expression (which I wish I could write instead of describe) is the sum of the odd numbers 1, 3, 5, ... 23, which adds up to 144, which is 12 squared. (Partly because 12 is on top.) Again, you probably already knew this.
My guess for number 3 is based on the second one. Represent each number in that list (i.e. 2, 5, 6 & 9) in binary, and "add" the corresponding digits; that is, use the last digit as values of D, as it were, the third digit for C, and so on. Ex. 0101 + 1100 = 1101. This is just my guess. Sorry I can't be more helpful.
For number 4, Capital Pi is the same thing, except it's iterated multiplication. Problem is, now I can't come up with _any_ sensible explanation. Sorry.
-- Dude. One weird.
To construct a truth table, establish columns for each of the variables and, if needed, their complements, and enter all combinations of TRUE and FALSE for the variables:
A | B | C | D |
--------------- T | T | T | T | T | T | T | F | T | T | F | T | T | T | F | F | T | F | T | T | T | F | T | F | T | F | F | T | T | F | F | F | F | T | T | T | F | T | T | F | F | T | F | T | F | T | F | F | F | F | T | T | F | F | T | F | F | F | F | T | F | F | F | F |
If you need it for visualization, add the complements:
A | A!| B | B!| C | C!| D | D'|
------------------------------- T | F | T | F | T | F | T | F | T | F | T | F | T | F | F | T | T | F | T | F | F | T | T | F | T | F | T | F | F | T | F | T | T | F | F | T | T | F | F | T | ...............................
Now the product terms go in, and there values calculated:
A | B | C | D |AB'CD'|ABC'D|A'BC'D'|A'B'CD|
--------------------------------------------------- T | T | T | T | F | F | F | F | T | T | T | F | F | F | F | F | T | T | F | T | F | T | F | F | T | T | F | F | F | F | F | F | T | F | T | T | F | F | F | F | T | F | T | F | T | F | F | F | T | F | F | T | etc. T | F | F | F | F | T | T | T | F | T | T | F | F | T | F | T | F | T | F | F | F | F | T | T | F | F | T | F | F | F | F | T | F | F | F | F |
Note that only one product term on each line can be TRUE. Once you have the product terms, you can probably find the sum terms on your own. If not, ask again. I don't even know the meaning of 3. and 4.
Jerry
How about:
Sigma m(2.5.6.9) is the "sum" or OR of the terms corresponding to the numbers 2 = 0010, 5 = 0101, 6 = 0110, 9 = 1001
Pi M(0,7,10,11) is the (product of sums) form (0000).(0111).(1010).(1011) - this usually invooves an inversion somewhere along the line.
I'm pretty sure about the sigma form being (sum of products) but look up Product of Sums for the second.
Bruce.
BIGEYE wrote:
The notation used for (3) is "Sum of minterms" form. Usually capital sigma is used to represent the sumation process. Thus your problem is the sum of minterms 2,5,6 and 9. In terms of variables A,B,C and D the function is: F = /A/BC/D+/AB/CD+/ABC/D+A/B/CD
The notation used in (4) is "Product of maxterms" form. Usually capital pi is used to represent these products. So your problem is the product of Maxterms
0,7,10 and 11. Again using variables A,B,C and D F = (A+B+C+D)(A+/B+/C+D)(/A+B+/C+D)(/A+B+/C+/D)NB: /A = NOT A
I hope that helps. You will find this stuff covered in most standard texts on Digital/Logic Design eg any of the Digital Design books by M. Morris Mano.
This explanation is correct for the most part but let me extrapolate i assume this is something to do with logic so the sigma is a sum of products expression ie. E (2,3,4) in a four variable table would be
0010 0011 0100 or corresponding to x1,x2,x3,x4 (x2)+(x3*x4)+(x2) the Pi type symbol is a POS (product of sums) and is the same idea except it is (a+b+c)*(d*e*f)......hope that helped
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