What is the output for the following logic circuit?

In summary, the conversation discusses a problem and its solution involving a circuit with gates and inputs A, B, and C. The original solution was incorrect and did not properly take into account the input C. The correct solution is A'+B+C'. The conversation also mentions an errata for a study guide that did not include this correction and was issued in 2017. The individual has decided to flag the problem and move on.
  • #1
icesalmon
270
13
Homework Statement
What is the output for the following logic circuit?
Relevant Equations
DeMorgan's Law
Logical Operations involving Logic Gates
I obtained the following result:
([(A xor B) xor 0]* AC)'
([(A'B + AB') xor (0)]*AC)'
[([A'B + AB']*(0)' + 0)*AC)]'
[(A'B + AB')*(1)*(AC)]'
[A'ABC + AB'AC]'
[AB'C]'
A'+B+C'
the solution to this problem is getting a different answer, I don't know why this solution isn't inverting the output AB'C
 

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  • #2
I agree with your answer. I think the simplest way to see that the given answer is wrong is to consider how C appears in it. The only appearance of C is as an input to the final NAND. It seems that +C' must be in the correct answer.
 
  • #3
FactChecker said:
I think the simplest way to see that the given answer is wrong

I was looking back and forth and at the given answer and wondering if the circuit and the explanation actually even go together. The explanation says the second gate is a NOR and the last gate is an AND but that's not what's drawn.

Code:
module problem2;
wire A,B,C,out;
reg [2:0] x;
assign out = !( A & C & (0^(A^B)) );
assign {A,B,C}=x[2:0];
initial begin
  $display("A B C | O");
  x=0;
  do begin
    #1 $display("%b %b %b | %b",A,B,C,out);
    x=x+1;
  end while(x!=0);
end
endmodule

Which yields A'+B+C'

Code:
A B C | O
0 0 0 | 1
0 0 1 | 1
0 1 0 | 1
0 1 1 | 1
1 0 0 | 1
1 0 1 | 0
1 1 0 | 1
1 1 1 | 1
 
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  • #4
the errata for a study guide I'm using to prepare for the Fundamentals of Engineering Exam didn't include this correction and was issued in 2017 so I decided to ask here. The solution I included corresponded to the problem I posted in the study guide, I'm not sure what happened with the solution to this problem when it was written. But I'm convinced this is a mistake. Thanks for the help in verifying that it was a mistake, i'll just flag the problem and move on.
 
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Related to What is the output for the following logic circuit?

What is the output for the following logic circuit?

The output for a logic circuit depends on the specific inputs and the logic gates used in the circuit. Without knowing the specific circuit and inputs, it is impossible to determine the output.

How do I determine the output for a logic circuit?

To determine the output for a logic circuit, you need to understand the logic gates used in the circuit and how they operate. Then, you can analyze the inputs and use the truth tables for each gate to determine the output.

What are the different types of logic gates?

There are several types of logic gates, including AND, OR, NOT, NAND, NOR, and XOR gates. Each gate has a different logic function and can be combined to create more complex logic circuits.

What is the purpose of a logic circuit?

The purpose of a logic circuit is to process and manipulate binary inputs to produce a desired output. They are commonly used in digital electronics and computer systems to perform logical operations.

Can logic circuits be used for more than just binary inputs?

While logic circuits are primarily used for binary inputs, they can also be designed to process multi-valued inputs. This can be achieved by using multiple logic gates and designing the circuit accordingly.

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