Circuit related doubt in digital logic

Question

Given circuit is to be implemented with minimum number of 2 input NAND & NOR Gates.. Tell the minimum number of NAND NOR GATES required.. 

1. 1,4
2. 4,1
3. 2,4
4. None

Comments

2,4?

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No it's 1,4 but I don't know how ?

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Then ans is wrong, or None

as we can produce this circuit in even 2 nor and 1 NAND GATE but i went with the ansof 2,4 as we can also do that,

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How did you make it with 2 NOR?

Answer 1

$((XY')' YZ)'$

$= XY' + Y' + Z'$

$= Y'(1+X) + Z'$

$= Y' +Z'$

$= (YZ)'$

$\therefore$ we need only $1$ NAND gate to implement the above circuit.

Also we can make NAND gate using $4$ NOR gates.

So we need $4$ NOR gates to implement the above circuit.

$\therefore$ Option $A$ is the correct answer.

Comments

Can you please help me in understanding the concept of these circuits ? Specially the NOR circuit.. this is really confusing

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watch the video lectures of neso academy on youtube.

NOR and NAND are universal gates so you can make any circuit from it. thats why in such questions they ask how many nand or nor gates are required to make the circuit.

first write the equation of the given circuit

then just try to convert the equation in terms of (xy)' or (x+y)' i.e. Not AND and Not OR forms and then count how many (xy)' or (x+y)' are there in the equation. This will be equal to the number of gates required.

Answer 2

Solution:-