Digital Electronics - Boolean Algebra and Logic Simplification - Discussion

Discussion Forum : Boolean Algebra and Logic Simplification - General Questions (Q.No. 14)
14.
How many gates would be required to implement the following Boolean expression before simplification? XY + X(X + Z) + Y(X + Z)
1
2
4
5
Answer: Option
Explanation:
No answer description is available. Let's discuss.
Discussion:
28 comments Page 1 of 3.

Nidhya said:   1 decade ago
My answer is C. on reducing the given exp we will get XY+XX+XZ+YX+YZ. here XY=YX; XX is nothing but X itself. X+XY+YX=X+XY=X(Y+1). so XZ - 1 gate YZ -1gate then for adding them - 2 gates. totally 4.

RANU said:   1 decade ago
XY requires 1 AND gate.. X(X+Z) requires 1 OR gate & 1 AND gate ..similarly Y(X+Z) require only 1 gate i.e. AND gate since X+Z operation already done and finally XY + X(X + Z) + Y(X + Z) can use one 3 input OR gate for ORing each operation ,hence only 5 gates are required without simplification.

Nandan said:   1 decade ago
Using K-map ,you get X+Y+Z, giving 2 gates. So answer is B

Shubhangi_n said:   1 decade ago
Answer is D as they want before simplification. Nidhya solved it after simplification.

Retheesh said:   1 decade ago
Answer is D.

Because it is required 4 gates for its individual operation and a final gate is required to make its sum.

So it is require toital- 5 gates.

Ramso said:   1 decade ago
The answer is 5, first it become xy+(x+y)(y+z)

It need 2 and gate and 3 or gate.

Xin said:   1 decade ago
The problem didn't require simplification by just simply counting the operation.

1. XY
2. X+Z
3. X(X + Z)
4. (X + Z)
5. Y(X + Z)

So the answer is 5.

BONDs said:   1 decade ago
Shouldn't it be 6.
Because,

1. X+Z (let's say Q).
2. XY.
3. XQ.
4. YQ.

5 and 6. 2+3+4.

Ram93 said:   1 decade ago
P:xy - 2 input AND.
Q:x+z - 2 input OR.
R:xQ - 2 input AND.
S:yQ - 2 input AND.

P+R+S - 3 input OR.

Total logic gates 5.

Hema said:   10 years ago
Perfectly the answer is C means 4 gates.

Inputs are xyz.

xy-1 AND gate.

z and x to OR gate gives x+z.

Then, x+z and y to AND gate gives why (x+z).

Finally, xy, (x+z) and y(x+z) should connect to OR gate.

So totally 4 gates i.e., 2 OR gates and 2 AND gates.


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