# Simplifying a boolean expression

Discussion in 'Homework Help' started by kadomori, Jan 29, 2011.

Jan 29, 2011
6
0
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 ..

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'

2. ### Papabravo Expert

Feb 24, 2006
10,135
1,786
Why do you think that additional simplifications are possible?
Isn't the purpose of the Karnaugh map to identify possible simplifications?

Jan 29, 2011
6
0
so it isn't really possible to simplify all of these expressions .. because it is already simplified .. thanks ..

4. ### Papabravo Expert

Feb 24, 2006
10,135
1,786
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.

5. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
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.