Simplifying a boolean expression

Thread Starter

kadomori

Joined Jan 29, 2011
6
i'm trying to make a binary to seven segment converter without using the 74LS47 decoder , i used the karnaugh mapping to analayze the formula for the output , just help me out in simplifying this boolean expressions .. :confused:




A = cb + d'b + da' + c'a' + d'ca + dc'b'
B = c'a' + c'b' + d'ba + db'a + d'b'a'
C = b'a+ d'a + dc' + d'c + c'b'
D = d'ba' + d'c'b + dc'a + cb'a + dca' + c'b'a'
E = ba' + db+ dc + c'a'
F = db + dc' + ca' + b'a' + d'cb'
G = d + c'b +ca' + cb'
 

Papabravo

Joined Feb 24, 2006
13,759
Why do you think that additional simplifications are possible?
Isn't the purpose of the Karnaugh map to identify possible simplifications?
 

Papabravo

Joined Feb 24, 2006
13,759
I don't know that for a fact since I did not look at the expressions closely. I was only asking a rhetorical question since the purpose of using a Karnaugh Map is to identify simplification possibilities. One could of course use other methods such as Quine-McCluskey (aka the method of prime implicants) to confirm the supposition that there are no further simplifications.
 

Georacer

Joined Nov 25, 2009
5,182
From a theoretical perspective, we can say that the expression is simple "enough". However, in real life you may have to take into account other factors, such as the type of gates available.

For your solution, you are good to go if you have a 4-input OR and 2 input AND gates.
But if all you have is a 3-input OR, you might want to make some factorizations.
 
Boolean algebra
a) simplify X=AB+ABC+ABCDE+ABCDEF
b) given that F=A'B'+C'+D'+E'.what is F
c) simplify X=A'B'C'D'+A'B'C'D+A'BCD+ABC'D+ABCD+AB'CD
i) using k maps
ii) by factorisations




0
 

Analog Ground

Joined Apr 24, 2019
397
Another level of minimization is to look for common terms between the outputs. Interestingly, in the internal logic diagram of an 74x47, no output has more than three product terms. Can this be reconciled with the equations from the thread starter? I would want to see his K-maps.
 

Analog Ground

Joined Apr 24, 2019
397
Another issue is terms 10 to 15. Are they don't cares? Do they form letters? Do they match the 74x47? Are your outputs active low like the 74x47 or active high?
 
Last edited:

Analog Ground

Joined Apr 24, 2019
397
I don't know that for a fact since I did not look at the expressions closely. I was only asking a rhetorical question since the purpose of using a Karnaugh Map is to identify simplification possibilities. One could of course use other methods such as Quine-McCluskey (aka the method of prime implicants) to confirm the supposition that there are no further simplifications.
Many K-maps do not have a single "best" solution. There is not enough info to work this problem.
 

MrAl

Joined Jun 17, 2014
7,604
Hi,

The question is do you want to use single level logic or multi level logic.
Single level will be the fastest, although for a real life LED display it probable does not matter and multi level logic will probably lead to the least number of gates.

If you really want to get simple, use a PROM. That's one single chip that will do it all once programmed with all the logic statements. I think you can also use two smaller PROMs.
 

dl324

Joined Mar 30, 2015
10,764
This was a 9 year old thread until it was bumped by a new member. The thread starter was last on AAC in 2014. I doubt s/he is still looking for an answer.
 

MrAl

Joined Jun 17, 2014
7,604
This was a 9 year old thread until it was bumped by a new member. The thread starter was last on AAC in 2014. I doubt s/he is still looking for an answer.
Hi,

Wow yeah i missed that too somehow. I guess i just saw the previous first few posts.
Well maybe if some poor lost soul wanders in here it might help them :)
 
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