- #1
electronic engineer
- 145
- 3
was asked to simplify this logic expression using Quinne-Mccluskey algorithm:
f=ABC'+ACD'+A'B'D+B'CD+A'C'D
need help!
thanks in advance!
f=ABC'+ACD'+A'B'D+B'CD+A'C'D
need help!
thanks in advance!
berkeman said:You're making me dizzy!
matejhowell said:How did you get the PI of 0xx1?
You cannot combine these two. The first term (00x1) does not depend on the variable C. The second term (0x01) does depend on the variable C. A similar argument can be made for the variable B. So, 0xx1 is not a Prime Implicant.by combining 00x1 , 0x01 so i got 00x1
matejhowell said:You cannot combine these two. The first term (00x1) does not depend on the variable C. The second term (0x01) does depend on the variable C. A similar argument can be made for the variable B. So, 0xx1 is not a Prime Implicant.
For Quine McCluskey, you can only combine terms that differ in one variable, not including don't cares.
I'll add more later. Tell me what you think.
matejhowell said:Hey.
My name is Matthew Howell, I'm living in Pensacola, FL. In a week I will have a bachelor's of computer engineering. I'm 22 I also have dial-up, so that is why my replies are so sparse. But we have time to work. Sorry I can't add more, but I am working out the problem and the next post should be the solution plus work.
_ ABCD|F
-------+-
0 0000|0
1 0001|1 A'B'D, A'C'D
2 0010|0
3 0011|1 A'B'D, B'CD
4 0100|0
5 0101|1 A'C'D
6 0110|0
7 0111|0
8 1000|0
9 1001|0
10 1010|1 ACD'
11 1011|1 B'CD
12 1100|1 ABC'
13 1101|1 ABC'
14 1110|1 ACD'
15 1111|0
Ones | Term | ABCD | Grad? | Terms | ABCD
-----+------+------+-------+ -------+-----
1 | 1 | 0001 | Yes | 1, 3 | 00-1
-----+------+------+-------+ 1, 5 | 0-01
2 | 3 | 0011 | Yes | -------+-----
_ | 5 | 0101 | Yes | 3, 11 | -011
_ | 10 | 1010 | Yes | 5, 13 | -101
_ | 12 | 1100 | Yes | 10, 11 | 101-
-----+------+------+-------+ 10, 14 | 1-10
3 | 11 | 1011 | Yes | 12, 13 | 110-
_ | 13 | 1101 | Yes | 12, 14 | 11-0
_ | 14 | 1110 | Yes |
PI's | 1 3 5 10 11 12 13 14
-------+------------------------
1, 3 | X X
1, 5 | X X
3, 11 | X X
5, 13 | X X
10, 11 | X X
10, 14 | X X
12, 13 | X X
12, 14 | X X
1, 3 ==> 00-1 ==> A'B'D
5, 13 ==> -101 ==> BC'D
10, 11 ==> 101- ==> AB'C
12, 14 ==> 11-0 ==> ABD'
PI's | 1 3 5 10 11 12 13 14
-------+------------------------
1, 3 | * *
1, 5 | * *
3, 11 | * *
5, 13 | * *
10, 11 | * *
10, 14 | * *
12, 13 | * *
12, 14 | * *
Quinne-McCluskey simplification is a method used to simplify boolean expressions with multiple variables. It is named after the mathematicians Edward J. Quinne and Stephen McCluskey.
This method is commonly used in digital logic design and computer science to simplify complex boolean expressions and reduce the number of logic gates needed to implement a circuit.
The process involves grouping terms together based on the number of variables they have in common and then combining these groups to eliminate redundant terms. This is done using a systematic approach and results in a simplified expression with the fewest possible terms.
Quinne-McCluskey simplification works best for expressions with a relatively small number of variables (less than 10). It may become more complex and time-consuming for larger expressions. Additionally, some expressions may not be fully simplified using this method.
Yes, there are other methods such as Karnaugh maps, algebraic manipulation, and the use of boolean identities. Each method may be more suitable for different types of expressions and it is important to understand and be proficient in multiple methods for simplification.