Simplest Logic Circuit for z=0 with Inputs a, b, c

In summary, the conversation discusses how to draw the simplest logic gate or circuit for a given description, where the inputs are a, b, and c and the output is z. It is determined that z=0 only if abc=010 or abc=110. The conversation also includes a discussion about simplifying the answer algebraically and checking it with a Karnaugh map. The final answer is given as z=0 if ##\bar a b \bar c\ +\ ab\bar c##.
  • #1
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Homework Statement



Draw the simplest logic gate or circuit for the description below. The inputs are ##a, b, c## and the output is ##z##.

##z = 0## only if ##abc = 010## or ##abc = 110##

Homework Equations

The Attempt at a Solution



So i drew up a quick table, AND and OR'ed the required terms together and came up with this:

IMG_0503.jpg


Is this okay? The input ##a## seems to have disappeared, which makes no sense to me. Unless its some sort of trick question where I only need 2 inputs since the output doesn't rely on ##a## at all.
 
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  • #2
Have you tried checking your answer with a Karnaugh map? I get a different answer...
 
  • #3
Also, have you tried plugging the two values back into your answer...?
 
  • #4
I'm trying to do this without a K-Map.

Plugging the values of ##b## and ##c## into my answer does provide the correct output, but I am unsure about the input ##a##.

I don't believe the answer is correct, and I am unsure how to algebraically simplify this if my above attempt is incorrect.
 
  • #5
My apolgies! I missed in your OP that z=0 for those two terms. Your answer does look correct. Sorry for any confusion I caused...
 
  • #6
berkeman said:
My apolgies! I missed in your OP that z=0 for those two terms. Your answer does look correct. Sorry for any confusion I caused...

Thank you for the clear up. I was just slightly confused about the inputs, but the logic worked out that way I guess.
 
  • #7
Zondrina said:
z= 0 only if abc=010abc = 010 or abc=110
You did well. An alternative is to write ##\bar z\ =\ \bar a b \bar c\ +\ ab\bar c##

Then simplify this as you did with your expression earlier, to get z = ...

The answers will be the same. :)
 

1. What is a logic circuit?

A logic circuit is an electronic circuit that performs logical operations based on inputs and produces an output based on those inputs. It is commonly used in digital systems to process and manipulate binary data.

2. How do you design a logic circuit?

To design a logic circuit, you first need to determine the logical operations that need to be performed for the desired output. Then, you can use logic gates, such as AND, OR, and NOT gates, to create a circuit that implements those operations. Finally, you can test and refine the circuit to ensure it functions correctly.

3. 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 performs a specific logical operation and can be combined to create more complex circuits.

4. Can logic circuits be used for other purposes besides digital systems?

Yes, logic circuits can also be used for analog systems, such as in signal processing and control systems. They can also be used in computer programming and artificial intelligence.

5. What are some common applications of logic circuits?

Logic circuits are used in a variety of electronic devices and systems, including computers, calculators, traffic lights, and home appliances. They are also used in industrial automation, telecommunications, and robotics.

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