Can someone please help me with this logic circuit problem?

Aruwin · 2012-10-29T00:19:44+00:00

I need step by step explanation and solution to this question please, so I can answer others. In the set of inputs a,b,c, in the case there are 2 or more numbers of '1' in the set, it is designated 1, or else, it is designated 0. Consider that logical function f above. 1. Draw the truth table for f. 2. Find the simplest product-of-sum expression for f.

Can someone please help me with this logic circuit problem?

Aruwin
@aruwin-WQ7eeu

Updated: Oct 25, 2024

Views: 947

I need step by step explanation and solution to this question please, so I can answer others.

In the set of inputs a,b,c,
in the case there are 2 or more numbers of '1' in the set, it is designated 1, or else, it is designated 0.
Consider that logical function f above.

1. Draw the truth table for f.
2. Find the simplest product-of-sum expression for f.

0

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Jeffrey Arulraj

Member • Oct 29, 2012

Here this should help
A B C F max terms
0 0 0 0 A+B+C
0 0 1 0 A+B+C'
0 1 0 0 A+B'+C
0 1 1 1
1 0 0 0 A'+B+C
1 0 1 1
1 1 0 1
1 1 1 1

So the final expression for f is

f=(A+B+C).(A+B+C').(A+B'+C).(A'+B+C)

Do simplify it further if you want to friend

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Aruwin

Member • Oct 29, 2012

jeffrey samuel
Here this should help
A B C F max terms
0 0 0 0 A+B+C
0 0 1 0 A+B+C'
0 1 0 0 A+B'+C
0 1 1 1
1 0 0 0 A'+B+C
1 0 1 1
1 1 0 1
1 1 1 1

So the final expression for f is

f=(A+B+C).(A+B+C').(A+B'+C).(A'+B+C)

Do simplify it further if you want to friend
How to further simplify this function?
f= a'bc+ab'c+abc'+abc
= c(a'b + ab') + ab (c' + c)
=c(a'b + ab') + ab
I only got it up to here. How to simplify it into the most simple expression?

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Vishal Sharma

Member • Oct 29, 2012

Aruwin
How to further simplify this function?
f= a'bc+ab'c+abc'+abc
= c(a'b + ab') + ab (c' + c)
=c(a'b + ab') + ab
I only got it up to here. How to simplify it into the most simple expression?

I don't think you can simplify it further..
the next step will be writing XOR expression instead of a'b+ab'
i.e. c (a XOR b) + ab

(You can replace the XOR by this sign too)

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Jeffrey Arulraj

Member • Oct 30, 2012

I think this is the most simplified form the Answer can ever get

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